*mbx* 42cf5a6900000000 1-Jan-2002 09:47:18 -0400,1043;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jan 2002 09:47:18 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16LPE9-00066y-00 for categories-list@mta.ca; Tue, 01 Jan 2002 09:45:13 -0400 Date: Tue, 1 Jan 2002 17:28:45 +1100 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Message-Id: <200201010628.g016Sjf322764@milan.maths.usyd.edu.au> To: categories@mta.ca Subject: categories: two categories Sender: cat-dist@mta.ca Precedence: bulk Thanks to Jack Duskin and John Baez for describing the point of Peter's comment that I had stupidly missed; I didn't associate "..." with a verbal pause. Other writers to the Bulletin Board have already vividly described the fires, but confirmed that no lives have been lost. Most years have fires around Sydney, but it's some time since they were as bad as this year. None of the category people, I think, lives in an area likely to be in danger. Thanks for your expressions of concern. Max. 1-Jan-2002 19:29:16 -0400,2146;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jan 2002 19:29:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16LYCj-0005tm-00 for categories-list@mta.ca; Tue, 01 Jan 2002 19:20:21 -0400 Date: Tue, 1 Jan 2002 10:28:12 -0500 (EST) From: JAMES STASHEFF X-Sender: stasheff@login3.isis.unc.edu To: categories@mta.ca Subject: categories: Re: Two categories or 2-categories? In-Reply-To: <200112310855.fBV8tun306897@milan.maths.usyd.edu.au> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Just saw the movie last night and was alert to the `two' problem more problematic to me was the whole phrase functor (some preposition) 2 categories between? sounded more like `in'?? .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds On Mon, 31 Dec 2001, Max Kelly wrote: > I don't know quite what Peter's point is here: there is no difference between > the spoken forms of "2-categories" and "two-categories". I think we all write > "2-categories", as we write "n-categories" and "w-categories", where I am > making-do with "w" for a lower-case Greek omega. Yet Blackwell, Power, and I, > when we considered general questions about the algebras for 2-monads and the > various kinds of strict and non-strict morphisms of these and some adjunctions > between the 2-categories that arise, entitled our paper "Two-dimensional monad > theory". I don't think "2-monad theory" would have represented our concerns as > well, being capable of interpretation as meaning a wider study than ours, or a > narrower one, depending on how it was taken by the reader. To the Australian > Research Council, such work is described as research on two-dimensional > universal algebra. > > What do others think? > > Regards - Max. > > > > > 1-Jan-2002 19:29:19 -0400,1240;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jan 2002 19:29:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16LYDR-0000Ai-00 for categories-list@mta.ca; Tue, 01 Jan 2002 19:21:05 -0400 Content-Type: text/plain; charset="iso-8859-1" From: David Yetter To: categories@mta.ca Date: Tue, 1 Jan 2002 09:53:52 -0600 X-Mailer: KMail [version 1.2] MIME-Version: 1.0 Message-Id: <0201010953270M.04532@debian> Content-Transfer-Encoding: 8bit Subject: categories: 2-categories and two categories Sender: cat-dist@mta.ca Precedence: bulk Actually I think there is an audible difference between the way native speakers of English (of whatever dialect) pronounce 2-categories and two categories, just as there is a subtle difference between the way the White House (the American presidential mansion), the white house (a residence of like color) and even the White house (where the White family reside) are pronounced. The phenomenon is called a "superfix" by linguists. (And once again, categorist in their idle moments show linguistics to be their favorite hobby.) Best Thoughts to all, David Yetter 2-Jan-2002 16:13:16 -0400,1734;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 Jan 2002 16:13:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Lrjd-0007c5-00 for categories-list@mta.ca; Wed, 02 Jan 2002 16:11:38 -0400 Date: Wed, 2 Jan 2002 09:19:27 -0500 (EST) From: JAMES STASHEFF X-Sender: stasheff@login1.isis.unc.edu To: categories@mta.ca Subject: categories: Re: 2-categories and two categories In-Reply-To: <0201010953270M.04532@debian> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk on being made to think that hard, I guess I do detect a difference \in my syllabic emPHAsis but in the movie I'm not even sure of the word preceding 2!! .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds On Tue, 1 Jan 2002, David Yetter wrote: > Actually I think there is an audible difference between the way native > speakers of English (of whatever dialect) pronounce 2-categories and two > categories, just as there is a subtle difference between the way the White > House (the American presidential mansion), the white house (a residence of > like color) and even the White house (where the White family reside) are > pronounced. > > The phenomenon is called a "superfix" by linguists. (And once again, > categorist in their idle moments show linguistics to be their favorite hobby.) > > Best Thoughts to all, > David Yetter > > > > 2-Jan-2002 16:13:21 -0400,1033;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 Jan 2002 16:13:21 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16LriY-0001qo-00 for categories-list@mta.ca; Wed, 02 Jan 2002 16:10:30 -0400 Message-ID: <3C330E24.4020905@bu.edu> Date: Wed, 02 Jan 2002 08:41:56 -0500 From: Saul Youssef Organization: Boston University User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:0.9.4) Gecko/20011126 Netscape6/6.2.1 X-Accept-Language: en-us MIME-Version: 1.0 To: Categories list Subject: categories: Home pages References: Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk I've collected home pages of recent posters to this list here: http://physics.bu.edu/~youssef/links/categories_home.html Happy new years all around, Saul Youssef 3-Jan-2002 13:31:21 -0400,4030;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 03 Jan 2002 13:31:21 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16MBbI-0000Ca-00 for categories-list@mta.ca; Thu, 03 Jan 2002 13:24:20 -0400 Mime-Version: 1.0 X-Sender: street@hera.ics.mq.edu.au Message-Id: Date: Thu, 3 Jan 2002 12:48:31 +1100 To: categories@mta.ca From: Ross Street Subject: categories: Natural and non-natural transformations Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk I would like to thank the many kind friends who have asked about the fires in Sydney. As you would know from news reports, thanks to the incredible work of the official fire fighters and volunteers, no human lives have been lost by burning. (One tired fire fighter was killed by his 4WD falling on him while he was repairing it.) After Max wrote, the situation deteriorated, particularly from the Macquarie University viewpoint. New Years Day a fire broke out (arson suspected) in the Lane Cove valley between the University and my house in Turramurra. This was very reminiscent of late December 1993: Todd Trimble had just arrived at Macquarie, we were walking to the Union Building for lunch, and saw the smoke billowing out of the Valley. This time I was at home, about 3 kilometres away, so could see the smoke clearly again. That night with the smell of smoke and sounds of sirens we told ourselves that most property losses have been adjacent to large bush reserves, national parks, etc. But I have also seen, in Santa Barbara, how eucalypt fires can consume 500 suburban houses in half an hour. Yesterday I came to work wondering whether my usual road home would be cut off by the gusty hot westerly winds, while Alf van der Poorten was wondering whether the fire would reach his street as it did in 1993-4. Macquarie University sounded like a war zone with choppers (including a big American one called Elvis) filling up with water from the little lake on campus. One of my vacation scholars who started today says he was told to prepare to evacuate. They seem to speak of three categories: out of control, contained, and under control. Fires don't seem to go out absolutely unless there is considerable rain. None is predicted. The fire mentioned above is now said to be under control. This happy news is no doubt helped largely by the local resident fire group that was formed and trained after the 1994 fires. Today I am able to concentrate on my work. Unfortunately the story north, west and south (there is no east) of Sydney is not so good. At Sussex Inlet and Jervis Bay (near Nowra) the fires are out of control. For a week or so the number of houses lost stood at 150. But more were destroyed last night, at least 20, but accurate figures were not known this morning because the fire is still raging, too hot, windy and smokey even for choppers. Warrimoo in the mountains west of Sydney has had a bad time. One of our neighbours has a son, with wife and two daughters, who lost their house. We just found out that Ron Andrews (from our Department) who moved to Warrimoo is okay. Murray Adelman (retired Macquarie category theorist) lives at Blackheath in the mountains, but I think that area is okay. The fires north of Sydney continue to breach containment lines. It is an ongoing disaster for plants and animals, and a continuing threat to people. However, the Sydney weather is not as hot as in 1994. Today is around 28 degrees C. This should help somewhat. Mike Barr also asked how our friends in Buffalo are fairing. Is there any word? I guess we cannot blame 7 ft of snow directly on crazy individuals; but is the worldwide crazy weather really natural Mr Bush? Let's continue to hope for a Happy New Year to all, Ross 3-Jan-2002 16:16:33 -0400,1996;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 03 Jan 2002 16:16:33 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16MEEo-0005M1-00 for categories-list@mta.ca; Thu, 03 Jan 2002 16:13:18 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 3 Jan 2002 14:36:24 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Natural and non-natural transformations In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Interesting letter from Ross. I do not know what to make of people who would start fires. There is arson here too, but it is almost invariably for insurance, a way of going out of business. Deplorable, but at least there is a comprehensible (if reprehensible) reason. I got a private note from Jack Duskin, saying in effect that they were just all the year's snowfall in one week, that they were digging out, used to it in any case, and things were gradually improving. He added that it was nothing like our ice storm four years ago (was it really that long ago?) And our ice storm was nothing like these fires. Although there were a few deaths (maybe five or six), a couple living two blocks away, 93 and 94 years old died from a fire that they started obviously to keep warm. A neighborhood of theirs whom I knew (he is a professor of German) told me that he had begged them to go to the town hall where emergency shelters had been set up, but they refused. Anyway, I am glad to hear there has been no loss of life in Sydney. (There were severe and totally unwonted snow storms down south in which people unused to driving in snow did die.) Michael 5-Jan-2002 11:46:00 -0400,2148;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 Jan 2002 11:46:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16MsrN-00007q-00 for categories-list@mta.ca; Sat, 05 Jan 2002 11:35:49 -0400 Mime-Version: 1.0 X-Sender: duskin@mail.buffnet.net Message-Id: Date: Thu, 3 Jan 2002 16:54:21 -0500 To: categories@mta.ca From: John Duskin Subject: categories: Buffalo Snow and "A Beautiful Mind" Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk -- Before our moderator cuts us off, here's the note I sent to Ross: With an average snowfall of 93 inches(236 cm)/season, we did get an all time record amount of snow. We had no snow in November (almost a record), and no snow in December, until...the evening of December 24, when it started and didn't stop until it had deposited 83 inches (211 cm) in the city by December 29 (!). White Christmas indeed. Thanks to the National Guard and outside contractors who put 500 pieces of equipment in service to supplement our 40, we are digging out and hauling the stuff away. But really, a snowstorm even like this is merely an inconvenience, nothing like the ice storm Montreal had a few years ago where Mike Barr ended up living in his Math Department office, much less a flood or a hurricane or burning houses, or even terrorists mailing mad cow disease. In Buffalo (as quoted in the New York Times) we say "fuggedaboudit !". Merry Christmas and Happy New Year to all! Jack Incidentally, I'm going to take John Isbell to "A Beautiful Mind" tomorrow. He was at Princeton with Nash and was consulted by the author of the book on which the film is (apparently, quite loosely) based. Can any of you who have already seen it tell me exactly where in the film the conversation with the student which ends with the notorious "functors..(two or 2-)categories" line comes? I would like to be ready to try to play very close attention when it comes! 5-Jan-2002 11:46:03 -0400,2193;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 Jan 2002 11:46:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Mssc-00007z-00 for categories-list@mta.ca; Sat, 05 Jan 2002 11:37:06 -0400 Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 4 Jan 2002 14:17:08 +0100 To: categories@mta.ca From: grandis@dima.unige.it (Marco Grandis) Subject: categories: Preprint: Higher fundamental groupoids for spaces Sender: cat-dist@mta.ca Precedence: bulk The following preprint is available: M. Grandis, Higher fundamental groupoids for spaces, Dip. Mat. Univ. Genova, Preprint 447 (Jan 2002). (17 p.) ftp://www.dima.unige.it/Home/grandis/public/HGpd.ps Abstract. Fundamental n-groupoids for a topological space are introduced, by techniques based on Moore paths, similar to those used in a previous paper for symmetric simplicial sets (M. Grandis, Higher fundamental functors for simplicial sets, Cahiers Topologie Geom. Differentielle Categ. 42 (2001), 101-136). Also the 'directed case' is treated, based on a structure recently introduced: a 'directed topological space', where privileged directions are assigned and paths need not be reversible (M. Grandis, Directed homotopy theory, I. The fundamental category, Dip. Mat. Univ. Genova, Preprint 443). Such objects are provided here with fundamental n-categories, as it was done for ordinary simplicial sets in the first cited paper. We end by comparing the present structures with the previous ones, via a geometric realisation of symmetric and ordinary simplicial sets, as spaces and directed spaces, respectively. All this essentially agrees also with the classical treatment of Kan complexes as non-directed structures. _____ Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ ftp://www.dima.unige.it/Home/grandis/public/ 5-Jan-2002 11:46:06 -0400,1960;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 Jan 2002 11:46:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16MsvZ-00008I-00 for categories-list@mta.ca; Sat, 05 Jan 2002 11:40:09 -0400 Date: Fri, 4 Jan 2002 09:22:17 -0800 (PST) From: jdolan@math.ucr.edu Message-Id: <200201041722.g04HMHC27882@yasky.ucr.edu> To: categories@mta.ca Subject: categories: adjoining an indeterminate Sender: cat-dist@mta.ca Precedence: bulk in lambek and scott's "introduction to higher order categorical logic", in the "historical comments" on section 7 of part 1, on page 116, they say: "it should be emphasized that, as long as equalizers are excluded from the definition of cartesian closed categories, adjoining an indeterminate of type a is not the same as forming the slice category c/a, but it is once equalizers are included. the latter was observed by grothendieck and joyal (see part 2, section 16, exercise 2)." i've been having a bit of trouble trying to understand exactly what they mean here. as far as i can tell, the mentioned "exercise 2" concerns the case where the category c is a topos, but the above quoted statement makes it sound like the equivalence between adjoining an indeterminate and forming a slice category should hold in the case where c is just a "cartesian closed category with equalizers", or something like that. offhand though i couldn't think of a way to get a result along these lines to be true. for one thing, the assumption that c has finite limits and exponentials doesn't even seem to compel the slice category c/a to have exponentials. (i think the category of co-commutative co-algebras over a field provides a counterexample.) can someone explain where i'm making a mistake here? or is it just that lambek and scott were only referring to the topos case, as discussed in their "exercise 2"? 5-Jan-2002 11:46:09 -0400,4930;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 Jan 2002 11:46:09 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16MswO-00008i-00 for categories-list@mta.ca; Sat, 05 Jan 2002 11:41:00 -0400 Date: Fri, 4 Jan 2002 17:26:03 GMT X-Authentication-Warning: toolo.dcs.ed.ac.uk: csl02 set sender to csl02+calls@dcs.ed.ac.uk using -f Message-ID: From: CSL02 To: categories@mta.ca Subject: categories: CFP: Computer Science Logic 2002 (CSL'02) Sender: cat-dist@mta.ca Precedence: bulk [ We apologize for the inevitable multiple copies of this announcement. Please see the note on mailing lists at the end. ] [ There is a PostScript copy of this Call at http://www.dcs.ed.ac.uk/csl02/CSL02-cfp1.ps for display on notice boards. ] Call for Papers Annual Conference of the European Association for Computer Science Logic CSL'02 22--25 September 2002, Edinburgh, UK Computer Science Logic (CSL) is the annual conference of the European Association for Computer Science Logic (EACSL). The conference is intended for computer scientists whose research activities involve logic, as well as for logicians working on issues significant for computer science. Suggested topics of interest include: automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, linear logic, logical aspects of computational complexity, finite model theory, higher order logic, logic programming and constraints, lambda and combinatory calculi, logical foundations of programming paradigms, modal and temporal logics, model checking, functions of program development (specification, extraction, transformation...), categorical logic and topological semantics, domain theory, database theory. The following will deliver invited lectures: Susumu HAYASHI (Kobe), on "Limit-Computable Mathematics and its Applications" Frank NEVEN (Limburg), on "Foundations of Query Languages for XML" Damian NIWINSKI (Warsaw), on mu-calculus The proceedings of the conference will be published in the Springer Lecture Notes in Computer Science series. Submitted papers must describe work not previously published. They must not be submitted concurrently to another conference with refereed proceedings. Research that is already submitted to a journal may be submitted to CSL, provided that (a) the PC chair is notified in advance that this is the case, and (b) it is not scheduled for journal publication before the conference. Papers authored or coauthored by members of the Programme Committee are not allowed. Papers should preferably be submitted either in LNCS format or in 12pt A4 format. Papers should not exceed 15 pages; full proofs may appear in a technical appendix which will be read at the reviewers' discretion. The title page must contain: title and authors; physical and e-mail addresses; identification of corresponding author, if not the first author; an abstract of no more than 200 words; a list of keywords. The key dates for the conference are: Submission: The submission process is in two stages, both with strict deadlines: 29 March 2002 for the title and abstract, and 7 April 2002 for the full text. Notification: 2 June 2002 Final copy due: 21 June 2002 Intending authors should check the conference Web page for any subsequent changes to these dates. Further information on all aspects of the conference will be found on the conference Web page: http://www.dcs.ed.ac.uk/csl02/ Programme Committee: Thorsten Altenkirch (U. Nottingham); Rajeev Alur (U. Pennsylvania); Michael Benedikt (Bell Labs); Julian Bradfield (U. Edinburgh (Chair)); Anuj Dawar (U. Cambridge); Yoram Hirshfeld (U. Tel Aviv); Ulrich Kohlenbach (U. Aarhus); Johann Makowsky (Technion Haifa); Dale Miller (Pennsylvania State U.); Luke Ong (U. Oxford); Frank Pfenning (Carnegie Mellon U.); Philippe Schnoebelen (ENS Cachan); Luc Segoufin (INRIA Rocquencourt); Alex Simpson (U. Edinburgh); Thomas Streicher (T.U. Darmstadt). [ Note on mailing lists. The To: header in each copy of this message contains the entry in our mailing list to which it was sent. If you wish the entry to be removed from our list, or have any problem with the mail, please contact csl02+calls@dcs.ed.ac.uk . For convenience in deleting duplicates, all copies of this message have the same message-id of . ] 5-Jan-2002 11:46:12 -0400,974;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 05 Jan 2002 11:46:12 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Mswg-00008w-00 for categories-list@mta.ca; Sat, 05 Jan 2002 11:41:18 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 4 Jan 2002 13:04:18 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Haskell, the language Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk I call your attention to the web site http://www.haskell.org/bookshelf/ What I found especially interesting was the last section (Foundations) of this page. Thanks to Noson Yanofsky for bringing this to my attention. 6-Jan-2002 10:19:55 -0400,9913;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 10:19:55 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NE4c-00020v-00 for categories-list@mta.ca; Sun, 06 Jan 2002 10:14:54 -0400 Message-ID: <3C35D51B.6A85F4E5@lim.univ-mrs.fr> Date: Fri, 04 Jan 2002 16:15:23 +0000 From: belaid benhamou X-Mailer: Mozilla 4.61 [en] (X11; I; Linux 2.2.13-7mdk i686) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CFP: AISC'2002 References: <200106291139.NAA04474@fandango.cs.unitn.it> Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-MIME-Autoconverted: from 8bit to quoted-printable by gyptis2.univ-mrs.fr id g04GBmO04792 Sender: cat-dist@mta.ca Precedence: bulk "Apologizes for multiple copies" *************************************************************************= *** * Call for Papers = * * AISC'2002 = * * Sixth International Conference on = * * ARTIFICIAL INTELLIGENCE AND SYMBOLIC COMPUTATION = * * Theory, Implementations and Applications = * * * (In conjunction with CALCULEMUS'2002) = * * * France, Marseille = * * July 1th-5th, 2002 = * *************************************************************************= *** Organized by: Universite de Provence, Universite de Mideterrannee, Faculte des sciences de Saint-Jerome, and the LSIS laborat= ory. More informations are available on the web site of the conference: http://www.cmi.univ-mrs.fr/aisc2002. -------------------------------------------------------------------------= ---- ABOUT THIS CONFERENCE SERIES ---------------------------- Conferences in this series are held every two years. The previous five took place in Karlsruhe (Germany), Cambridge (United Kingdom), Steyr (Austria), Plattsburgh (USA) and Madrid (Spain)-- the first three under t= he name "Artificial Intelligence and Symbolic Mathematical Computing (AISMC)= ". For the year 2002, the conference AISC will be held in Marseille (France)= in conjunction with CALCULEMUS'2002 (The 10th Symposium on the Integration o= f symbolic Computation and Mechanized Reasoning). The aim of the conference is to make a forum for the exchange of ideas on artificial intelligence and symbolic computation. The purpoose of such discussion is to provide new tools and solutions by considering problem solving methods from AI and symbolic (mathematical) computation. Another = goal is to make personal contacts among researchers from different fields rela= ted to AI and Symbolic Computation. The conference is concerned with all aspe= cts of research (including theory, implementations and applications). ORGANIZERS OF AISC'2002 / CALCULEMUS'2002 ----------------------------------------- Both AISC'2002 and CALCULEMUS'2002 are organized by the three Universitie= s of Marseille: L'universite de Provence (Aix-Marseille I), L'universite de la Miditerrann=E9e (Aix-Marseille II), la Facult=E9 des sciences de Saint-Je= rome (Aix-Marseille III) and the LSIS laboratory. TOPICS ------ * AI and Symbolic Mathematical Computing * Computer Algebra Systems and Automated Theorem Provers * Integration of Logical Reasoning and Computer Algebra * Engineering, Industrial and Operations Research Applications * Foundations and Complexity of Symbolic Computation * Mathematical Modeling of Multi-Agent Systems * Programming Languages for Symbolic Computation * Symbolic Computations for Expert Systems and Machine Learning * Implementations of Symbolic Computation Systems * Logic and Symbolic Computing * Constraint Programming * Term Rewriting * Logic based Multi Agent Systems * Reasoning Papers on other topics with strong links to those descibed above will als= o be welcomed for consideration. The second and the third topics of the previo= us liste fit perfectly the scope of CALCULEMUS'2002. STEERING COMMITTEE ------------------ Jacques Calmet (Univ. Karlsruhe, Germany) John Campbell (University College London, England) Eugenio Roanes-Lozano (Univ. Complutense de Madrid, Spain) CHAIRS ------- Belaid Benhamou (Conference chair) Universite de Provence CMI, 39 rue F. Juliot-Curie 13453 Marseille Cedex 13, France email:Belaid.Benhamou@cmi.univ-mrs.fr Laurent Henocque (Program chair) Universite de Mediterrannee ESIL, 163 Avenue de Luminy Marseille Cedex 09, France email:henocque@esil.univ-mrs.fr PROGRAM COMMITTEE ----------------- Luigia C. Aiello (Univ. La Sapienza, Roma, Italy) Jose A. Alonso (Univ. de Sevilla, Spain) Michael Beeson (San Jose State Univ., USA) Belaid Benhamou (Universite de Provence, France) Greg Butler (Univ. Concordia, Montreal, Canada) Jim Cunningham (Imperial College London, UK) James Davenport (Univ. of Bath, England) Carl van Geem (LAAS-CNRS, Tolouse, France) Reiner Haehnle (Univ. of technology, Chalmers, Sweden) Deepak Kapur (Univ. New Mexico, USA) Luis M. Laita (Univ. Politecnica de Madrid, Spain) Luis de Ledesma (Univ. Politecnica de Madrid, Spain) Eric Monfroy (Univ de Nantes, France) Jose Mira (UNED, Spain) Ewa Orlowska (Inst. Telecomunications, Warsaw, Poland) Jochen Pfalzgraf (Univ. Salzburg, Austria) Jan Plaza (Univ. Plattsburgh, USA) Zbigniew W. Ras (Univ. North Carolina, Charlotte, USA) Tomas Recio (Univ. de Santander, Spain) Peder Thusgaard Ruhoff (MDS, Proteomics, Denmark) Pierre Siegel (Universite de Provence, France) Andrzej Skowron (Warsaw Univ., Poland) John Slaney (ANU, Canberra, Australia) Viorica Sofronie-Stokkermans (Max Planck Institut, Germany) Karel Stokkermans (Univ. Salzburg, Austria) Carolyn Talcott (Stanford Univ., USA) Rich Thomason (Univ. of Pittsburgh, USA) Dongming Wang (Univ. Paris VI, France) LOCAL COMMITTEE --------------- Gilles Audemard (Univ. Univ de Provence, Aix-Marseille I) Belaid Benhamou (Univ. Univ de Provence, Aix-Marseille I) Philippe Jegou (Univ. de Saint Jerome, Aix-Marseille III) Laurent Henocques (Univ. de la Mediterrann=E9e, Aix-Marseille I= I) Pierre Siegel (Univ. Univ de Provence,Aix-Marseille I) Eric Wurbel (Univ. du Var, Toulon) DEADLINES --------- * Deadline for submission: February 15, 2002 * Notification of acceptance: March 30, 2002 * Camera-ready papers due: April 19, 2002 PROCEEDINGS ----------- Papers submitted to the conference undergo a standard review process. Previous proceedings were printed by Springer-Verlag (in their volumes LN= CS 737, 958, 1138, LNAI 1476 and LNAI 1930). This year's proceedings will al= so be published by Springer-Verlag and will be available at the conference. SUBMISSION REQUIREMENTS ----------------------- Theoretical and applied research papers on all topics within the scope of the conference are encouraged. Submitted papers (in English) must not exc= eed 12 pages in length. The title page should contain the title, author(s) with affiliation(s), e-mail address(es), a listing of keywords and abstract PL= US the topics from the list above to which the paper is related. The program committee will subject all submitted papers to peer review. Theoretical papers will be judged on their originality and contribution t= o their field and applied papers on the importance and originality of the application. Results must be unpublished. Electronic submission is strong= ly encouraged. Please send a postscript file (.PS ) by e-mail to both "aisc2002@cmi.univ-mrs.fr" and "henocque@esil.univ-mrs.fr". If electronic submission is not possible, please send four hard copies to the address g= iven at the end. SUBMISSION REQUIREMENTS FOR THE FINAL VERSION OF ACCEPTED PAPERS ---------------------------------------------------------------- (Observe that this section does not apply when submitting the papers; it REFERS only to the final version of ACCEPTED papers. Nevertheless papers = can be submitted in final format, although for submission only the .PS should= be sent) Accepted papers should be prepared in LaTeX and formatted in accordanc= e to the instructions given for Springer-Verlag's LNAI series (the correspo= n- ding style files can be obtained from the web page http://www.springer.de/comp/lncs/authors.html and are the same for the LNCS and LNAI). Please remember to send, together with the .TEX, any non-standard files that are necessary to compile the LaTeX source code too. ADDRESSES (ORGANIZATION) ------------------------ e-mail: aisc2002@cmi.univ-mrs.fr web page: http://www.cmi.univ_mrs.fr/aisc2002 Surface mail: AISC 2002 Dr. Belaid Benhamou Universite de Provence, CMI, 39 rue F. Juliot-Curie 13453 Cedex 13 Phone number: (+33) 4 91 11 36 22 Fax number: (+33) 4 91 11 36 02 6-Jan-2002 10:19:58 -0400,2787;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 10:19:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NE6a-0002DP-00 for categories-list@mta.ca; Sun, 06 Jan 2002 10:16:56 -0400 Date: Sat, 5 Jan 2002 16:51:16 +0000 (GMT) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: Re: adjoining an indeterminate In-Reply-To: <200201041722.g04HMHC27882@yasky.ucr.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *16Mu2Q-0006zk-00*rt.tRzKJDNM* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk On Fri, 4 Jan 2002 jdolan@math.ucr.edu wrote: > in lambek and scott's "introduction to higher order categorical > logic", in the "historical comments" on section 7 of part 1, on page > 116, they say: > > "it should be emphasized that, as long as equalizers are excluded from > the definition of cartesian closed categories, adjoining an > indeterminate of type a is not the same as forming the slice category > c/a, but it is once equalizers are included. the latter was observed > by grothendieck and joyal (see part 2, section 16, exercise 2)." > > i've been having a bit of trouble trying to understand exactly what > they mean here. as far as i can tell, the mentioned "exercise 2" > concerns the case where the category c is a topos, but the above > quoted statement makes it sound like the equivalence between adjoining > an indeterminate and forming a slice category should hold in the case > where c is just a "cartesian closed category with equalizers", or > something like that. offhand though i couldn't think of a way to get > a result along these lines to be true. for one thing, the assumption > that c has finite limits and exponentials doesn't even seem to compel > the slice category c/a to have exponentials. (i think the category of > co-commutative co-algebras over a field provides a counterexample.) > > can someone explain where i'm making a mistake here? or is it just > that lambek and scott were only referring to the topos case, as > discussed in their "exercise 2"? > Only Lambek and Scott can say what they meant by this remark. However, the result is true for arbitrary locally cartesian closed categories (i.e., if C is a lccc, then C/a is the free lccc-with-an-indeterminate- of-type-a generated by C); it doesn't need the extra structure of a topos. It is, of course, not true for `merely' cartesian closed categories with equalizers, precisely because under these hypotheses C/a needn't be cartesian closed. Peter Johnstone 6-Jan-2002 10:21:52 -0400,2121;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 10:21:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NE8a-0002SI-00 for categories-list@mta.ca; Sun, 06 Jan 2002 10:19:00 -0400 Message-ID: <001c01c19677$c3245f60$580f7aa8@saulworld> From: "Saul Youssef" To: References: Subject: categories: Re: "A Beautiful Mind" Date: Sat, 5 Jan 2002 22:02:45 -0800 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.50.4133.2400 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4133.2400 Sender: cat-dist@mta.ca Precedence: bulk I just this minute got back from seeing the movie. It's after Nash asks his friend (the one who beats him at Go) if he can hang around Princeton. There'll be a long pause and his friend will ask if Nash will be needing an office. It will happen soon after that in the library. The student will say: "The functor {bite of sandwich} two categories as he's pointing." It happens fairly late in the movie. It has something to do with covering spaces, so I'm guessing it's t-w-o categories. This would be just the group to be hallucinating 2-categories, that's for sure! The show was sold out in Harvard square by the way. The audience liked it & applauded at the end. It's really well acted, but I feel emotionally abused by the experience. Saul Youssef > > Incidentally, I'm going to take John Isbell to "A Beautiful Mind" > tomorrow. He was at Princeton with Nash and was consulted by the > author of the book on which the film is (apparently, quite loosely) > based. Can any of you who have already seen it tell me exactly where > in the film the conversation with the student which ends with the > notorious "functors..(two or 2-)categories" line comes? I would like > to be ready to try to play very close attention when it comes! > > > > 6-Jan-2002 10:22:01 -0400,1836;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 10:22:01 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NE9g-0002Tc-00 for categories-list@mta.ca; Sun, 06 Jan 2002 10:20:08 -0400 Date: Sun, 6 Jan 2002 14:24:06 +0100 From: Frank Atanassow To: Michael Barr Cc: Categories list Subject: categories: Re: Haskell, the language Message-ID: <20020106142406.A10006@cs.uu.nl> References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i In-Reply-To: ; from barr@barrs.org on Fri, Jan 04, 2002 at 01:04:18PM -0500 Sender: cat-dist@mta.ca Precedence: bulk Michael Barr wrote (on 04-01-02 13:04 -0500): > I call your attention to the web site > http://www.haskell.org/bookshelf/ > What I found especially interesting was the last section (Foundations) of > this page. Thanks to Noson Yanofsky for bringing this to my attention. In that case, you may also be interested to know I've linked your book from a site I maintain, Programming Language Theory Texts Online. http://www.cs.uu.nl/people/franka/ref There are several other texts there which will be familiar to many readers of this list. I announced this page once on the TYPES forum, but I wasn't sure at the time whether folks here would be interested also. Perhaps I was wrong? Take a look and tell me what you think. -- Frank Atanassow, Information & Computing Sciences, Utrecht University Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands Tel +31 (030) 253-3261 Fax +31 (030) 251-379 6-Jan-2002 10:25:44 -0400,3695;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 10:25:44 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NECM-0002eA-00 for categories-list@mta.ca; Sun, 06 Jan 2002 10:22:54 -0400 X-Received: from zent.mta.ca ([138.73.1.15]) by mailserv.mta.ca with smtp (Exim 3.33 #2) id 16N3zV-0008Vq-00 for cat-dist@mta.ca; Sat, 05 Jan 2002 23:28:57 -0400 X-Received: FROM mta5.snfc21.pbi.net BY zent.mta.ca ; Sat Jan 05 23:25:18 2002 -0400 X-Received: from computer1 ([63.193.118.205]) by mta5.snfc21.pbi.net (iPlanet Messaging Server 5.1 (built May 7 2001)) with ESMTP id <0GPH00LYLZ072G@mta5.snfc21.pbi.net> for cat-dist@mta.ca; Sat, 05 Jan 2002 19:28:55 -0800 (PST) Date: Sat, 05 Jan 2002 19:31:11 -0800 From: David Espinosa Subject: categories: Re: Haskell, the language In-reply-to: To: cat-dist@mta.ca Message-id: <000001c19662$96b1ca40$800a0a0a@computer1> MIME-version: 1.0 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 X-Mailer: Microsoft Outlook, Build 10.0.2627 Content-type: text/plain; charset=us-ascii Content-transfer-encoding: 7BIT Importance: Normal X-Priority: 3 (Normal) X-MSMail-priority: Normal Sender: cat-dist@mta.ca Precedence: bulk From: cat-dist@mta.ca [mailto:cat-dist@mta.ca] On Behalf Of Michael Barr Sent: Friday, January 04, 2002 10:04 AM I call your attention to the web site http://www.haskell.org/bookshelf/ What I found especially interesting was the last section (Foundations) of this page. Yes, category theory is now used fairly commonly in the separate but closely related fields of programming language semantics and functional programming. While we are citing references, here is one that I think pure mathematicians would find interesting: Richard Bird and Oege de Moor, Algebra of Programming, Prentice-Hall, 1997. Bird and De Moor apply algebras, coalgebras, and allegories to small-scale programming problems. See also the many papers by Lambert Meertens, who is one of the founders of this approach to "calculational programming". On the topic of programming languages, I would like to direct categorical logicians' attention to Lego, Cayenne, and Agda (and perhaps others). These languages implement Martin-Lof type theory with a universe hierarchy and are interesting because they combine programming language, proof system, and module system into a single type theory. Since these three functionalities are typically separate in most programming languages, combining them yields a significant three-for-one economy. Also, unlike most programming languages, these languages include dependent sums and products, which are used pervasively in standard mathematics. Indeed, it seems to me that Martin-Lof type theory closely achieves (one of) its original aims of modeling informal mathematical practice. The last chapter of Bart Jacobs, Categorical Logic and Type Theory, Elsevier, 1999. covers the categorical logic of this type theory but doesn't describe the universe hierarchy in detail (see page 691). Is there any work showing how to model a universe hierarchy categorically? I'm sure it would be clear if I really understood Jacobs, but that's a big if. And I am sure that many programming language researchers would appreciate a more tutorial presentation of the semantics of this type theory than appears in Jacobs' book. Andy Pitts and Martin Hoffman have some tutorial papers, but, in this case, more is better. David 6-Jan-2002 17:43:36 -0400,1433;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 17:43:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NL0F-0000O5-00 for categories-list@mta.ca; Sun, 06 Jan 2002 17:38:51 -0400 Date: Sun, 6 Jan 2002 10:06:29 -0500 (EST) From: Peter Freyd Message-Id: <200201061506.g06F6TY03879@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Go v Nash Sender: cat-dist@mta.ca Precedence: bulk Saul Youssef writes It's after Nash asks his friend (the one who beats him at Go) if he can hang around Princeton. Very minor point, but I suspect the film makers were aware that what Nash would be playing on a go board was the game still known at the Princeton math department in the 60s as the game of "nash". Eventually it became known that John Nash had not been the first to invent it, and the name changed to the now more familiar "hex". Does anyone remember, were the stones in the film on the squares or the intersection lines? (Usually, but not always, the game of nash, unlike go, was played on the squares, it being understood that they were really supposed to be hexagons -- with two diagonal connections besides the two vertical and two horizontal connections.) The film's Nash makes some remark to the effect that he's supposed to win -- clearly Nash should win at nash. 6-Jan-2002 17:43:39 -0400,2569;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 17:43:39 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NL0j-0008R8-00 for categories-list@mta.ca; Sun, 06 Jan 2002 17:39:21 -0400 Mime-Version: 1.0 X-Sender: duskin@mail.buffnet.net Message-Id: Date: Sun, 6 Jan 2002 11:33:34 -0500 To: categories@mta.ca From: John Duskin Subject: categories: Re: "A Beautiful Mind" Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk -- Many thanks to the many people who replied to my tangential query: Incidentally, I'm going to take John Isbell to "A Beautiful Mind" tomorrow. He was at Princeton with Nash and was consulted by the author of the book on which the film is (apparently, quite loosely) based. Can any of you who have already seen it tell me exactly where in the film the conversation with the student which ends with the notorious "functors..(two or 2-)categories" line comes? I would like to be ready to try to play very close attention when it comes! Fortunately, the information in Peter's original post turned out to be sufficiently precise for me to carefully listen when the scene occurred. The student says to Nash, "Galois extensions are really the same as covering spaces!" . Immediately afterward, the student (with a sandwich in his mouth) mumbles "functor(?)...two categories". Clearly, from the context he is explaining exactly what he means by "really the same", i.e., a (dual) equivalence of two categories, which is, of course, true. Of course, it would be amusing to have a line about 2-categories appearing in a Holywood film, but alas, we'll just have to wait. John was not feeling well at the afternoon time of the film, so I'll take him to it later if he still wants to go. But for this and the terrible weather he was quite enthusiastic to see it. Steve Schanuel, in particular, tells me how much he liked the film. It's certainly worth seeing. At the very least, it's a fascinating film cleverly exploring the contrast between a paranoid schizophrenic's view of reality and the rest of the world's view , even if it is only marginally related to, i.e., only " inspired by", actual events in John Nash's life. Incidentally, and off topic, does anyone know anything about this "presentation of fountain pens" tradition at Princeton? Best regards, Jack 6-Jan-2002 17:43:42 -0400,2587;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 17:43:42 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NL2h-0000WT-00 for categories-list@mta.ca; Sun, 06 Jan 2002 17:41:23 -0400 Date: Sun, 6 Jan 2002 14:53:52 -0500 (EST) From: JAMES STASHEFF X-Sender: stasheff@login7.isis.unc.edu To: categories@mta.ca Subject: categories: Re: "A Beautiful Mind" In-Reply-To: <001c01c19677$c3245f60$580f7aa8@saulworld> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk also sold out in suburban Philadelphia! ticket cashier seemed pleasantly surprised > It's really well acted, but I feel emotionally abused by the experience. as a mathematician or as a human being? insulin shock is not pleasant nor is paranoia .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds On Sat, 5 Jan 2002, Saul Youssef wrote: > > I just this minute got back from seeing the movie. > > It's after Nash asks his friend (the one who beats him at Go) if he can > hang around Princeton. There'll be a long pause and his friend will ask > if Nash will be needing an office. It will happen soon after that in the > library. The student will say: > > "The functor {bite of sandwich} two categories as he's pointing." > > It happens fairly late in the movie. > > It has something to do with covering spaces, so I'm guessing it's t-w-o > categories. This would be just the group to be hallucinating 2-categories, > that's for sure! > > The show was sold out in Harvard square by the way. The audience liked it > & applauded at the end. It's really well acted, but I feel emotionally > abused by the experience. > > Saul Youssef > > > > > Incidentally, I'm going to take John Isbell to "A Beautiful Mind" > > tomorrow. He was at Princeton with Nash and was consulted by the > > author of the book on which the film is (apparently, quite loosely) > > based. Can any of you who have already seen it tell me exactly where > > in the film the conversation with the student which ends with the > > notorious "functors..(two or 2-)categories" line comes? I would like > > to be ready to try to play very close attention when it comes! > > > > > > > > > > > > > 6-Jan-2002 17:43:46 -0400,1808;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 06 Jan 2002 17:43:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NL3r-0000cY-00 for categories-list@mta.ca; Sun, 06 Jan 2002 17:42:35 -0400 Message-ID: <3C37FF7B.8000306@kestrel.edu> Date: Sat, 05 Jan 2002 23:40:43 -0800 From: Dusko Pavlovic User-Agent: Mozilla/5.0 (Windows; U; Win98; en-US; rv:0.9.2) Gecko/20010726 Netscape6/6.1 X-Accept-Language: en-us MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: "A Beautiful Mind" References: <001c01c19677$c3245f60$580f7aa8@saulworld> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk i haven't seen the "beautiful mind" movie yet, but i did attend the DIMACS workshop on algorithmic mechanism design in october, and got a chance to speak to john nash! each and every talk went on about the nash equilibria and nash bargaining and nash this and nash that --- with nash in the second row all the time. i imagine he'll go to see the movie as well, and perhaps comment about the importance of go and functor two categories in his way. life is a big place, sometimes. -- dusko PS btw, i think the upshot of the SGA4 exercise cited by lambek and scott is that the argument given there shows that the polynomial category S[x^A] in Locally CCC is (equivalent to) S/A. funny enough, the polynomial category in CCC can then be viewed as the subcategory spanned by the second projections (which is, of course, isomorphic with the kleisly for the Ax(-) comonad) PPS i was surprised no one mentioned categories in "waking life". 7-Jan-2002 20:53:45 -0400,1111;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 20:53:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkTC-0001kz-00 for categories-list@mta.ca; Mon, 07 Jan 2002 20:50:26 -0400 Message-ID: <001f01c19782$9caf2070$90a3cec1@pcsabadini> From: "R F C Walters" To: Subject: categories: Paper on feedback Date: Mon, 7 Jan 2002 14:52:56 +0100 MIME-Version: 1.0 X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2919.6700 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2919.6700 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk In a previous letter where I gave my new address I also announced a paper "Feedback, trace and fixed-point semantics". By mistake, it was not actually available on my home page at the time. In any case an improved version is now available at http://www.unico.it/~walters/papers/fics.pdf Bob Walters 7-Jan-2002 20:53:45 -0400,1796;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 20:53:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkTy-0001uw-00 for categories-list@mta.ca; Mon, 07 Jan 2002 20:51:14 -0400 Message-ID: <3C39BCC2.2A4F083D@email.unc.edu> Date: Mon, 07 Jan 2002 10:20:34 -0500 From: Jim Stasheff X-Mailer: Mozilla 4.77 [en] (Windows NT 5.0; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Go v Nash References: <200201061506.g06F6TY03879@saul.cis.upenn.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk at Princeton, there was a true nash board also it works well on chinese checker board Peter Freyd wrote: > Saul Youssef writes > > It's after Nash asks his friend (the one who beats him at Go) if he > can hang around Princeton. > > Very minor point, but I suspect the film makers were aware that what > Nash would be playing on a go board was the game still known at the > Princeton math department in the 60s as the game of "nash". Eventually > it became known that John Nash had not been the first to invent it, > and the name changed to the now more familiar "hex". Does anyone > remember, were the stones in the film on the squares or the > intersection lines? (Usually, but not always, the game of nash, unlike > go, was played on the squares, it being understood that they were > really supposed to be hexagons -- with two diagonal connections > besides the two vertical and two horizontal connections.) The film's > Nash makes some remark to the effect that he's supposed to win -- > clearly Nash should win at nash. 7-Jan-2002 20:53:49 -0400,2088;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 20:53:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkQs-0001pc-00 for categories-list@mta.ca; Mon, 07 Jan 2002 20:48:02 -0400 Date: Sun, 6 Jan 2002 23:11:48 -0500 (EST) From: "P. Scott" Reply-To: "P. Scott" To: categories@mta.ca Subject: categories: Re: adjoining an indeterminate In-Reply-To: <200201041722.g04HMHC27882@yasky.ucr.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk On Fri, 4 Jan 2002 jdolan@math.ucr.edu wrote: > in lambek and scott's "introduction to higher order categorical > logic", in the "historical comments" on section 7 of part 1, on page > 116, they say: > > "it should be emphasized that, as long as equalizers are excluded from > the definition of cartesian closed categories, adjoining an > indeterminate of type a is not the same as forming the slice category > c/a, but it is once equalizers are included. the latter was observed > by grothendieck and joyal (see part 2, section 16, exercise 2)." > .............................. The remark was a bit loosely worded, but of course the exercise in question relates to the fact that in toposes (and still more generally in doctrines of ccc's with finite limits and for which slicing is well-behaved, e.g. locally ccc's) then one may interpret slicing as "adjoining an indeterminate". This is not the case for ordinary ccc's (no finite limits). For further info, see the exercises of L&S, p. 64. The reason for making the remark in the first place was that when Lambek and I used to lecture on ccc's long ago, and we used the word "indeterminate", someone from the audience would invariably say "oh, you mean take the slice category" and a long discussion would then ensue... Cheers, Phil Scott 7-Jan-2002 20:53:52 -0400,4756;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 20:53:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkRn-0001Xt-00 for categories-list@mta.ca; Mon, 07 Jan 2002 20:48:59 -0400 Message-Id: To: categories-list@mta.ca Date: Mon, 7 Jan 2002 01:57:46 -0800 (PST) From: Posina Venkata Rayudu Subject: categories: Re: Categories and cognition To: categories@mta.ca In-Reply-To: <5.1.0.14.1.20011222174255.009f3830@mailx.u-picardie.fr> MIME-Version: 1.0 Content-Type: text/plain; charset=3Dus-ascii Sender: cat-dist@mta.ca Precedence: bulk --- Andree Ehresmann wrote: > It uses categorical tools, e.g. completion theorems, > for explaining the=20 > emergence of higher order cognitive processes and > the formation of a=20 > Semantics (possibly without necessarily language). > http://perso.wanadoo.fr/vbm-ehr STRUCTURES AND THEIR PRESENTATION It appears that Prof. Ehresmann=92s category theoretic work on SEMANTICS WITHOUT LANGUAGE provides the necessary concretisation of the experiences mentioned by Prof. Wells (12/20/01) and Prof. Vickers (12/21/01) regarding concepts & words. Also Prof. Lawvere (12/3/01) has pointed that =91concepts=92 (at least in mathematics) can be construed as categories and that these algebraic structures are distinct from =91their presentations=92 (and yet closely related), which are needed to calculate various features of concepts. More importantly, he states that SKETCHES provide the algebraic framework necessary to mathematically capture the =91presentation of concept.=92 Can we bring this mathematical framework of concepts and their presentations in terms of categories and sketches to bear on what appears to be an analogous problem of concepts and language in cognitive science? Secondly, I was wondering whether the two approaches (Prof. Ehreshman & Prof. Lawvere) to the problem are same or different. It seems to me that the problem they are addressing is same (semantics & language, concepts & presentation). --- Steve Vickers wrote: >replacement of talking by pictorial concepts Sometimes our thinking is not in terms of words but is in terms of what appear like images (pictures, diagrams=85). According to Fodor, to the extent thinking =91says something=92 (proposition), the images in thinking can=92t be the kind of images we see (face of Mono Lisa). You can replace some words with pictures, but how are you going to make a sentence (that can take truth value; true or false) with pictures?=20 Thinking, based on introspection, has, at times, no words but has word-like-images (those =93images=94 that can be used as building blocks of propositions). Some of the devastating arguments against =91thinking can be imagery=92 (the kind you see on TV) are due to Wittgenstein. =93A picture which corresponds to a man walking up a hill forward corresponds equally, and in the same way, to a man sliding down the hill backward=94 (Fodor 1975, 1998). Pictures, by themselves, don=92t support propositions that take yes-or-no truth-values. A string (a concatenation) of images cannot replace well-formed formulae, assertion. I dare not speculate as to whether non-Boolean truth-value object of topos has any bearing on Wittgenstein=92s =91proof against pictures in thinking.=92=20 >diagrammatic metaphors (grab an object, place it somewhere, link it to other objects to handle certain events, etc.) get implemented in rather different ways in different languages. Given images are transformed into words, can we mathematically capture the process? (cf. Cartesian geometry) I would like to have your comments on the above. I am not sure where I stand in this debate; I don=92t even know =91the difference between the way a picture of a circle (black contour on white background) refers to the concept CIRCLE and the way the equation x^2 + y^2 =3D r^2 refers to the same concept CIRCLE?=92 Thanks so much for your time. Thanking you, Sincerely, Posina venkata rayudu Fodor (1975) The Language of Thought, HUP, Cambridge, pp. 174-195. Fodor (1998) When is a dog a DOG, Nature 396:325-327. You will love Fodor (or you will hate him). =3D=3D=3D=3D=3D Posina Venkata Rayudu C/o: Sri. S. S. Chalam Advocate & Notary Public H.No: 39-4-10, Innespeta Rajahmundry =96 533102 Andhra Pradesh, India Phone: 91 (0883) 444232 __________________________________________________ Do You Yahoo!? Send FREE video emails in Yahoo! Mail! http://promo.yahoo.com/videomail/ 7-Jan-2002 20:53:55 -0400,930;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 20:53:55 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkPY-0001lv-00 for categories-list@mta.ca; Mon, 07 Jan 2002 20:46:40 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Sun, 6 Jan 2002 17:27:36 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Antonia's Line Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Did anyone else see this movie? It was a beautiful movie and, while this was peripheral it did have one character giving a lecture on algebraic topology with a chain complex in it. 7-Jan-2002 20:53:58 -0400,1673;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 20:53:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkQC-0001lr-00 for categories-list@mta.ca; Mon, 07 Jan 2002 20:47:20 -0400 Message-ID: <3C38F0FC.77516FFF@it.uts.edu.au> Date: Mon, 07 Jan 2002 11:51:09 +1100 From: Barry Jay X-Mailer: Mozilla 4.77 [en] (X11; U; SunOS 5.8 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: Categories list Subject: categories: Re: Natural disasters References: Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Dear Michael, I'm just back from vacation. Thanks for asking how we're doing. The fires have been fierce around Sydney, with all the major roads cut from time to time, but surprisingly there has been no loss of life yet. We are expecting high temperatures and strong winds over the next few days but preparations appear to be in order. Best wishes to everyone for 2002, Barry Michael Barr wrote: > > It seems like there are natural disasters, first in Sydney and, to a > lesser extent, in Buffalo (82 inches of snow by one report) and I would > like to enquire how all are. > > Michael -- Associate Professor C.Barry Jay, Phone: (61 2) 9514 1814 Associate Dean (RPP), Faculty of IT www-staff.it.uts.edu.au/~cbj University of Technology, Sydney. CRICOS Provider 00099F 7-Jan-2002 21:06:40 -0400,2753;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 07 Jan 2002 21:06:40 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16NkiL-0002Yx-00 for categories-list@mta.ca; Mon, 07 Jan 2002 21:06:05 -0400 Message-ID: <3C3A1EA3.78E67B27@csc.liv.ac.uk> Date: Mon, 07 Jan 2002 22:18:11 +0000 From: Peter McBurney X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.4.9-12 i686) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Go v Nash References: <200201061506.g06F6TY03879@saul.cis.upenn.edu> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk [Note from moderator: The discussion of Nash, `A Beautiful Mind' and CT in the movies has been entertaining and informative, but does seem to be leading away from our central interest. For anyone so inclined, there is a very good Math in the Movies web site that is easily found. Therefore, I ask that posts not be made on the topic after tomorrow, January 8. Digests of side discussion sent for later posting are very welcome, with best wishes to all for 2002, Bob Rosebrugh] Peter Freyd wrote: > (Usually, but not always, the game of nash, unlike > go, was played on the squares, it being understood that they were > really supposed to be hexagons -- with two diagonal connections > besides the two vertical and two horizontal connections.) The film's > Nash makes some remark to the effect that he's supposed to win -- > clearly Nash should win at nash. I do not know this game of "Hex" (or "Nash"), but wouldn't there be 4 diagonal connections, not 2, from any square? Should not therefore the game be called "Oct", rather than "Hex"? -- Peter McBurney **************************************************************** Peter McBurney Agent Applications, Research and Technology (Agent ART) Group Department of Computer Science University of Liverpool Liverpool L69 7ZF U.K. Tel: + 44 151 794 6768 Email: P.J.McBurney@csc.liv.ac.uk Web page: www.csc.liv.ac.uk/~peter/ **************************************************************** 8-Jan-2002 18:58:31 -0400,1773;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 08 Jan 2002 18:58:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16O599-0003Oz-00 for categories-list@mta.ca; Tue, 08 Jan 2002 18:55:08 -0400 X-Authentication-Warning: triples.math.mcgill.ca: rags owned process doing -bs Date: Tue, 8 Jan 2002 02:35:00 -0500 (EST) From: "Robert A.G. Seely" To: Categories list Subject: categories: Re: Antonia's Line In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk I don't know if Bob is going to allow this (;-)) but I agree this is a beautiful movie, and has the rather nice scene Mike points out (he doesn't add that the category theory is in fact "foreplay"!). I seem to recall Peter Freyd mentionning this film a long time ago - I didn't pay much attention to Peter's post at the time, and bought a copy of Antonia's Line "on spec" from a remainder bin in a supermarket shop in Nova Scotia a few years back (at $4 it seemed a reasonable bet), and was quite surprised to come across the scene - only then recalling Peter's review. Probably the best $4 video I've ever bought! -= rags =- On Sun, 6 Jan 2002, Michael Barr wrote: > Did anyone else see this movie? It was a beautiful movie and, while this > was peripheral it did have one character giving a lecture on algebraic > topology with a chain complex in it. ================== R.A.G. Seely 8-Jan-2002 18:58:35 -0400,734;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 08 Jan 2002 18:58:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16O5B2-0003a0-00 for categories-list@mta.ca; Tue, 08 Jan 2002 18:57:04 -0400 Date: Tue, 8 Jan 2002 13:09:02 +0100 Message-Id: <200201081209.g08C92s04355@foobar.pps.jussieu.fr> From: Paul LEVY To: categories@mta.ca Subject: categories: lluf subcategory Sender: cat-dist@mta.ca Precedence: bulk Hi I've heard the term "lluf subcategory" meaning "subcategory with the same objects but possibly fewer morphisms". Is there a reference for this usage? Regards Paul http://www.pps.jussieu.fr/~levy/ 8-Jan-2002 18:58:38 -0400,2205;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 08 Jan 2002 18:58:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16O5AY-0003f1-00 for categories-list@mta.ca; Tue, 08 Jan 2002 18:56:34 -0400 Date: Tue, 8 Jan 2002 02:59:35 -0500 (EST) From: Peter Freyd Message-Id: <200201080759.g087xZK23143@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Re: Antonia's Line Sender: cat-dist@mta.ca Precedence: bulk Mike writes: Did anyone else see this movie? It was a beautiful movie and, while this was peripheral it did have one character giving a lecture on algebraic topology with a chain complex in it. The answer is Yes (the word "Line" was added in North America): From: Peter Freyd Date: Thu, 13 Jul 2000 16:33:03 -0400 (EDT) To: Categories list Subject: film functor The Dutch film "Antonia" written and directed by Marleen Gorris won the 1996 Oscar for best foreign language film. There's a scene in which the 20-year-old granddaughter of the title character is at a blackboard with a lot of exact sequences. She says (quoting the English subtitles): We will assume that the singular chain complex of the empty set equals zero. With theorem 5.8 this implies that the nth homology group is the same as the nth relative homology group if we take the subspace as the empty set. New we can construct a functor from the category....from the category Top to the category of chain complexes. Define the functor S* as follows: S* sends the ordered pair to the singular chain complex of the space X divided by the complex of A. Is this the first commercial film with categories and functors? (It's not the first with homological algebra: in 1980 "It's My Turn" opened with its lead at a blackboard proving the snake lemma.) It should be noted that the categories and functors in "Antonia" turn out to be foreplay: the speaker makes eye contact with a guy in her audience and the next scene instantly transports them from the classroom to the bedroom. 8-Jan-2002 18:59:10 -0400,33220;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 08 Jan 2002 18:59:10 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16O5Cv-0003cW-00 for categories-list@mta.ca; Tue, 08 Jan 2002 18:59:02 -0400 Date: Tue, 8 Jan 2002 08:38:05 -0500 (EST) From: Peter Freyd Message-Id: <200201081338.g08Dc5h00906@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: categorical incunabula Sender: cat-dist@mta.ca Precedence: bulk Herein is an attempt to list all MathSciNet publications through 1958 in that mention categories or functors. There are several obstructions. First of course is that we don't really want all mentions of categories. Besides the sense relevant to this email address there are the other mathematical senses (e.g. Baire, Lusternik-Schnirelmann), the ancestral logical sense, and, of course, the ordinary sense. It is not always completely clear which sense is being used in any given review, so some of this is a matter of judgment. (As examples of papers not included: 19,52d by Eilenberg and Tudor Ganea; and 21 #4425 by Ganea and P.J.Hilton. Both use the word "category" but only in the L-S sense. But all three authors were categorical in the relevant sense.) Next: MathSciNet when asked for all reviews that mention categories or functor "anywhere" often responds with reviews that look as iff they ought to be mentioning them but, in fact, do not. Very mysterious. I have included all these (the topics always look right.) Finally, the use of the words in the review may well be on the part of the categorically inclined reviewer, rather than the author. By all means tell me what should be changed. Most important, of course, are the omissions. I have been surprised by a number of things. First is the 1942 paper by Sammy and Saunders. Until now I had always assumed that both functors and categories saw the first light of published day in the 1945 paper. Functors are celebrating their 60th birthday! I have appended Weil's review of the 1942 paper. The first person on the list after Eilenberg and Mac Lane is S-T Hu. His 1947 paper defines "homotopy functor". I've appended Steenrod's review. Saunders's 1948 paper (without Sammy) first surprised me 40 years ago. Buchsbaum in his 1955 paper that introduced abelian categories (under the name "exact categories") said that he saw no way of defining infinite products. Which meant that he hadn't seen Saunders's 1948 paper. Is this the first appearance of universal mapping definitions? I've appended Philip Hall's review. The 1956 paper by Atiyah is remarkable: it is true categorical algebra. To quote Eilenberg's review (which I've appended) "The Krull-Schmidt theorem asserting the existence and essential uniqueness of direct sum decompositions into indecomposable factors is proved in [abelian categories] satisfying a suitable chain condition." In 1958 Andrew Gleason characterized the projective objects in the category of compact Hausdorff spaces. I've appended Dana Scott's review. (Which means that Dana was going categorical already as a grad student.) Most striking is the stellar nature of these early contributors and consumers of category theory. At the very end of this posting is a list of the 92 authors. (I count 4 Fields Medals, 3 National Medals of Science, 3 Wolf Prizes, 5 Cole Prizes and 10 Steele Prizes.) ********************************************************************** 1942 4,134d EILENBERG, SAMUEL; MAC LANE, SAUNDERS. Natural isomorphisms in group theory. Proc. Nat. Acad. Sci. U. S. A. 28, (1942). 537--543. 1945 7,109d EILENBERG, SAMUEL; MAC LANE, SAUNDERS. General theory of natural equivalences. Trans. Amer. Math. Soc. 58, (1945). 231--294. 1947 9,297h HU, SZE-TSEN. An exposition of the relative homotopy theory. Duke Math. J. 14, (1947). 991--1033. 1948 10,5e EILENBERG, SAMUEL; MAC LANE, SAUNDERS. Cohomology and Galois theory. I. Normality of algebras and Teichm|ller's cocycle. Trans. Amer. Math. Soc. 64, (1948). 1--20. 10,9c MAC LANE, SAUNDERS. Groups, categories and duality. Proc. Nat. Acad. Sci. U. S. A. 34, (1948). 263--267. 10,621d WEIL, ANDRI Variitis abiliennes et courbes algibriques. (French) Actualitis Sci. Ind., no. 1064 = Publ. Inst. Math. Univ. Strasbourg 8 (1946). Hermann & Cie., Paris, 1948 65 pp 1951 13,314c EILENBERG, SAMUEL; MAC LANE, SAUNDERS. Homology theories for multiplicative systems. Trans. Amer. Math. Soc. 71, (1951). 294--330. 13,440a CHEVALLEY, CLAUDE. Deux thiorhmes d'arithmitique. (French) J. Math. Soc. Japan 3, (1951). 36--44. 1952 14,398b EILENBERG, SAMUEL; STEENROD, NORMAN. Foundations of algebraic topology. Princeton University Press, Princeton, New Jersey, 1952. xv+328 pp. 1953 14,670b EILENBERG, SAMUEL; MAC LANE, SAUNDERS. Acyclic models. Amer. J. Math. 75, (1953). 189--199. 15,53a MORITA, KIITI. Cohomotopy groups for fully normal spaces. Sci. Rep. Tokyo Bunrika Daigaku. Sect. A. 4, (1953). 251--261. 16,563b KDHLER, ERICH. Algebra und Differentialrechnung. (German) Bericht |ber die Mathematiker-Tagung in Berlin, Januar, 1953, pp. 58--163. Deutscher Verlag der Wissenschaften, Berlin, 1953. 1954 15,816b KEESEE, JOHN W. Sets which separate spheres. Proc. Amer. Math. Soc. 5, (1954). 193--200. 16,391a EILENBERG, SAMUEL; MAC LANE, SAUNDERS. On the groups $H(.Pi,n)$. II. Methods of computation. Ann. of Math. (2) 60, (1954). 49--139. 16,442c EILENBERG, SAMUEL. Algebras of cohomologically finite dimension. Comment. Math. Helv. 28, (1954). 310--319. 1955 16,564g EILENBERG, SAMUEL; MAC LANE, SAUNDERS. On the homology theory of abelian groups. Canad. J. Math. 7, (1955). 43--53. 17,579a AUSLANDER, MAURICE. On the dimension of modules and algebras. III. Global dimension. Nagoya Math. J. 9 (1955), 67--77. 17,579b BUCHSBAUM, D. A. Exact categories and duality. Trans. Amer. Math. Soc. 80 (1955), 1--34. 17,763c GROTHENDIECK, ALEXANDRE. Produits tensoriels topologiques et espaces nucliaires. (French) Mem. Amer. Math. Soc. 1955 (1955), no. 16, 18,558B MAC LANE, SAUNDERS. Slide and torsion products for modules. Univ. e Politec. Torino. Rend. Sem. Mat. 15 (1955--56), 281--309. 19,974F DUGUNDJI, J. Remark on homotopy inverses. Portugal. Math. 14 (1955), 39--41. 1956 17,994b MILNOR, JOHN. Construction of universal bundles. I. Ann. of Math. (2) 63 (1956), 272--284. 17,1040e CARTAN, HENRI; EILENBERG, SAMUEL. Homological algebra. Princeton University Press, Princeton, N. J., 1956. xv+390 pp. 17,1118c WHITEHEAD, J. H. C. Duality in topology. J. London Math. Soc. 31 (1956), 134--148. 18,57a ARAKI, SHTRT. On Steenrod's reduced powers in singular homology theories. Mem. Fac. Sci. Ky{sy{ Univ. Ser. A. 9 (1956), 159--173. 18,142e KAN, DANIEL M. Abstract homotopy. II Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 255--258. 18,375d HARADA, MANABU. Note on the dimension of modules and algebras. J. Inst. Polytech. Osaka City Univ. Ser. A. 7 (1956), 17--27. 18,558c EILENBERG, SAMUEL. Homological dimension and syzygies. Ann. of Math. (2) 64 (1956), 328--336. 18,662c MCCANDLESS, BYRON H. Test spaces for dimension $n$. Proc. Amer. Math. Soc. 7 (1956), 1126--1130. 18,753b POSTNIKOV, M. M. Investigations in homotopy theory of continuous mappings. III. General theorems of extension and classification. (Russian) Mat. Sb. N.S. 40(82) (1956), 415--452. 19,172b ATIYAH, M. On the Krull-Schmidt theorem with application to sheaves. Bull. Soc. Math. France 84 (1956), 307--317. 19,440a KAN, DANIEL M. Abstract homotopy. III. Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 419--421. 19,522c Siminaire Paul Dubreil et Charles Pisot, 9e annie: 1955/56. Alghbre et thiorie des nombres. (French) Secritariat mathimatique, 11 rue Pierre Curie, Paris, 1956. ii+213 pp. 20 #1704 MORITA, KIITI; Tachikawa, Hiroyuki. Character modules, submodules of a free module, and quasi-Frobenius rings. Math. Z. 65 1956 20 #4204 DEDECKER, P. Quelques applications de la suite spectrale aux intigrales multiples du calcul des variations et aux invariants intigraux. II. (French) Bull. Soc. Roy. Sci. Lihge 25 1956 387--399. 1957 18,919b SPANIER, E. H.; WHITEHEAD, J. H. C. The theory of carriers and $S$-theory. Algebraic geometry and topology. A symposium in honor of S. Lefschetz, pp. 330--360. Princeton University Press, Princeton, N.J., 1957. 18,754c COPELAND, ARTHUR H., Jr. On $H$-spaces with two non-trivial homotopy groups. Proc. Amer. Math. Soc. 8 (1957), 184--191. 18,815d MILNOR, JOHN. The geometric realization of a semi-simplicial complex. Ann. of Math. (2) 65 (1957), 357--362. 19,160a GUGENHEIM, V. K. A. M.; MOORE, J. C. Acyclic models and fibre spaces. Trans. Amer. Math. Soc. 85 (1957), 265--306. 19,431d Siminaire "Sophus Lie" de la Faculti des Sciences de Paris, 1955-56. Hyperalghbres et groupes de Lie formels. (French) Secritariat mathimatique, 11 rue Pierre Curie, Paris, 1957. 61 pp. 19,759d FORRESTER, AMASA. Acyclic models and de Rham's theorem. Trans. Amer. Math. Soc. 85 (1957), 307--326. 19,759e Kan, Daniel M. On c. s. s. complexes. Amer. J. Math. 79 (1957), 449--476. 20 #892 MAC LANE, SAUNDERS. Homologie des anneaux et des modules. (French) 1957 Colloque de topologie algibrique, Louvain, 1956 pp. 55--80 Georges Thone, Lihge; Masson & Cie, Paris 20 #893 DIXMIER, J. Homologie des anneaux de Lie. (French) Ann. Sci. Ecole Norm. Sup. (3) 74 1957 25--83. 20 #894 MORITA, KIITI; Kawada, Yutaka; Tachikawa, Hiroyuki. On injective modules. Math. Z. 68 1957 217--226. 20 #896 ROSENKNOP, I. Z. On the H. Cartan algebra of a polynomial ideal. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 113 1957 1218--1221. 20 #923 ISBELL, J. R. Some remarks concerning categories and subspaces. Canad. J. Math. 9 1957 563--577. 20 #1705 HATTORI, AKIRA. On $.Lambda $-injectivity (problem 6.3.19). (Japanese) S{gaku 8 1956/1957 208--209. 20 #2392 EHRESMANN, CHARLES. Gattungen von lokalen Strukturen. (German) Jber. Deutsch. Math. Verein. 60 1957 Abt. 1, 49--77. 20 #2702 ZEEMAN, E. C. On the filtered differential group. Ann. of Math. (2) 66 1957 557--585. 20 #2703 KAN, DANIEL M. On the homotopy relation for c.s.s. maps. Bol. Soc. Mat. Mexicana 2 1957 75--81. 20 #2704 KAN, DANIEL M. On c.s.s. categories. Bol. Soc. Mat. Mexicana 2 1957 82--94. 20 #3201 BUCHSBAUM, DAVID. A survey of homological algebra. 1957 Report of a conference on linear algebras, June, 1956 pp. 53--59 National Academy of Sciences-National Research Council, Washington, Publ. 502 20 #3906 LEGER, GEORGE F., Jr. On cohomology of Lie algebras. Proc. Amer. Math. Soc. 8 1957 1010--1020. 20 #3907 SRIDHARAN, R. On some algebras of infinite cohomological dimension. J. Indian Math. Soc. (N.S.) 21 1957 179--183. 20 #4540 KUBOTA, TOMIO. Unit groups of cyclic extensions. Nagoya Math. J. 12 1957 221--229. 20 #4587 NAKAYAMA, TADASI. On modules of trivial cohomology over a finite group. II. Finitely generated modules. Nagoya Math. J. 12 1957 171--176. 20 #5229 EILENBERG, SAMUEL; ROSENBERG, ALEX; ZELINSKY, DANIEL. On the dimension of modules and algebras. VIII. Dimension of tensor products. Nagoya Math. J. 12 1957 71--93. 20 #5485 HELLER, ALEX. Twisted ranks and Euler characteristics. Illinois J. Math. 1 1957 562--564. 20 #6449 NAKAYAMA, TADASI. On the complete cohomology theory of Frobenius algebras. Osaka Math. J. 9 1957 165--187. 20 #6452 TAKASU, SATORU. On the change of rings in the homological algebra. J. Math. Soc. Japan 9 1957 315--329. 22 #1887 WYLIE, S. Intercept-finite cell complexes. 1957 Algebraic geometry and topology. A symposium in honor of S. Lefschetz pp. 389--399 Princeton University Press, Princeton, N.J. 20 #6449 NAKAYAMA, TADASI. On the complete cohomology theory of Frobenius algebras. Osaka Math. J. 9 1957 165--187. 20 #6452 TAKASU, SATORU. On the change of rings in the homological algebra. J. Math. Soc. Japan 9 1957 315--329. 21 #1328 GROTHENDIECK, ALEXANDER. Sur quelques points d'alghbre homologique. (French) Tthoku Math. J. (2) 9 1957 119--221. 21 #2675 AMITSUR, S. A. The radical of field extensions. Bull. Res. Council Israel. Sect. F 7F 1957/1958 1--10. 21 #4417 PETERSON, FRANKLIN P. Functional cohomology operations. Trans. Amer. Math. Soc. 86 1957 197--211. 22 #12127 Siminaire A. Grothendieck; 1re annie: 1957. Alghbre homologique. (French) Secritariat mathimatique, 11 rue Pierre Curie, Paris 1958 42 pp. (mimeogiaphed). 23 #A3163 LOONSTRA, F. Erweiterungen von Grenzgruppen. (German) Nederl. Akad. Wetensch. Proc. Ser. A 60 = Indag. Math. 19 1957 548--559. 23 #A3579 NAKAMURA, TOKUSI. Minimal complexes of fibre spaces. J. Math. Soc. Japan 9 1957 1--19. 25 #109 GOPALAKRISHNAN, N. S.; RAMABHADRAN, N.; Sridharan, R. A note on the dimension of modules and algebras. J. Indian Math. Soc. (N.S.) 21 1957 185--192. 1958 20 #895 TACHIKAWA, HIROYUKI. Duality theorem of character modules for rings with minimum condition. Math. Z. 68 1958 479--487. 20 #1661 BUZBY, B.; WHAPLES, G. Quadratic forms over arbitrary fields. Proc. Amer. Math. Soc. 9(1958), 335--339; erratum 10 1958 174. 20 #1712 GRIFFITHS, H. B. On limits of systems of groups. Proc. Amer. Math. Soc. 9 1958 118--129. 20 #2393 OHKUMA, TADASHI. Duality in mathematical structure. Proc. Japan Acad. 34 1958 6--10. 20 #2705 SHIH, WEISHU. Sur la suite exacte d'homotopie. (French) C. R. Acad. Sci. Paris 246 1958 2833--2835. 20 #3183 MORITA, KIITI. Duality for modules and its applications to the theory of rings with minimum condition. Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 1958 83--142. 20 #3202 DOLD, ALBRECHT; Puppe, Dieter. Non-additive functors, their derived functors, and the suspension homomorphism. Proc. Nat. Acad. Sci. U.S.A. 44 1958 1065--1068. 20 #3203 AUSLANDER, MAURICE; BUCHSBAUM, DAVID A. Homological dimension in noetherian rings. II. Trans. Amer. Math. Soc. 88 1958 194--206. 20 #3537 DOLD, ALBRECHT. Homology of symmetric products and other functors of complexes. Ann. of Math. (2) 68 1958 54--80. 20 #3805 MAL.CPRIME CEV, A. I. Defining relations in categories. (Russian) Dokl. Akad. Nauk SSSR 119 1958 1095--1098. 20 #4257 GUTIIRREZ-BURZACO, MARIO. Extension of uniform homotopies. Nederl. Akad. Wetensch. Proc. Ser. A 61 = Indag. Math. 20 1958 61--69. 20 #4262 BAUER, FRIEDRICH-WILHELM. .ber Fortsetzungen von Homologiestrukturen. (German) Math. Ann. 135 1958 93--114. 20 #4264 BRAHANA, THOMAS R. Axioms for local homology theory. Duke Math. J. 25 1958 381--399. 20 #4588 HILTON, P. J. Homotopy theory of modules and duality. 1958 Symposium internacional de topologma algebraica International symposium on algebraic topology pp. 273--281 Universidad Nacional Autsnoma de Mixico and UNESCO, Mexico City 20 #4658 CARTAN, HENRI. Espaces fibris analytiques. (French) 1958 Symposium internacional de topologma algebraica International symposium on algebraic topology pp. 97--121 Universidad Nacional Autsnoma de Mixico and UNESCO, Mexico City 20 #4837 CARTAN, HENRI; Eilenberg, Samuel. Foundations of fibre bundles. 1958 Symposium internacional de toplogma algebraica International symposium on algebraic topology pp. 16--23 Universidad Nacional Autsnoma de Mixico and UNESCO, Mexico City 20 #5192 AURORA, SILVIO. On power multiplicative norms. Amer. J. Math. 80 1958 879--894. 20 #5194 NORTHCOTT, D. G. A note on polynomial rings. J. London Math. Soc. 33 1958 36--39. 20 #5228 MAC LANE, SAUNDERS. Extensions and obstructions for rings. Illinois J. Math. 2 1958 316--345. 20 #5800 MATLIS, EBEN. Injective modules over Noetherian rings. Pacific J. Math. 8 1958 511--528. 20 #5979 SPENCER, D. C. A spectral resolution of complex structure. 1958 Symposium internacional de topologma algebraica International symposium on algebraic topology pp. 68--76 Universidad Nacional Autsnoma de Mixico and UNESCO, Mexico City 20 #6092 MILNOR, John. The Steenrod algebra and its dual. Ann. of Math. (2) 67 1958 150--171. 20 #6414 AUSLANDER, MAURICE; BUCHSBAUM, DAVID A. Codimension and multiplicity. Ann. of Math. (2) 68 1958 625--657. 20 #6450 NAKAYAMA, TADASI. Note on complete cohomology of a quasi-Frobenius algebra. Nagoya Math. J. 13 1958 115--121. 20 #6451 HOCHSCHILD, G. Note on relative homological dimension. Nagoya Math. J. 13 1958 89--94. 20 #6453 KAPLANSKY, IRVING. Projective modules. Ann. of Math (2) 68 1958 372--377. 20 #6460 BAER, REINHOLD. Die Torsionsuntergruppe einer Abelschen Gruppe. (German) Math. Ann. 135 1958 219--234. 20 #6461 ERDVS, JENV. On the splitting problem of mixed abelian groups. Publ. Math. Debrecen 5 1958 364--377. 20 #6694 ECKMANN, BENO; HILTON, PETER J. Groupes d'homotopie et dualiti. Groupes absolus. (French) C. R. Acad. Sci. Paris 246 1958 2444--2447. 20 #6698 PUPPE, DIETER. Homotopiemengen und ihre induzierten Abbildungen. I. (German) Math. Z. 69 1958 299--344. 20 #7045 HARADA, MANABU; KANZAKI, Teruo. On Kronecker products of primitive algebras. J. Inst. Polytech. Osaka City Univ. Ser. A 9 1958 19--28. 20 #7048 BER.V STE.U.I N, ISRAKL. On the dimension of modules and algebras. IX. Direct limits. Nagoya Math. J. 13 1958 83--84. 20 #7049 KAPLANSKY, IRVING. On the dimension of modules and algebras. X. A right hereditary ring which is not left hereditary. Nagoya Math. J. 13 1958 85--88. 20 #7050a HILTON, P. J.; LEDERMANN, W. Homology and ringoids. I. Proc. Cambridge Philos. Soc. 54 1958 152--167. 20 #7050b HILTON, P. J.; LEDERMANN, W. Homological ringoids. Colloq. Math. 6 1958 177--186. 20 #7051 HELLER, ALEX. Homological algebra in abelian categories. Ann. of Math. (2) 68 1958 484--525. 21 #77 NORGUET, FRANGOIS. Sur l'homologie associie ` une famille de dirivations. (French) C. R. Acad. Sci. Paris 247 1958 1081--1083. 21 #79 HARADA, MANABU. The weak dimension of algebras and its applications. J. Inst. Polytech. Osaka City Univ. Ser. A 9 1958 47--58. 21 #1317 HARADA, MANABU. A note on Hattori's theorems. J. Inst. Polytech. Osaka City Univ. Ser. A 9 1958 43--45. 21 #1583 GODEMENT, ROGER. Topologie algibrique et thiorie des faisceaux. (French) Actualit'es Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13 Hermann, Paris 1958 viii+283 pp. 21 #1598 .V SVARC, A. S. The genus of a fiber space. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 119 1958 219--222. 21 #2233 WHITEHEAD, J. H. C. Duality between $CW$-lattices. 1958 Symposium internacional de topologma algebraica International symposi um on algebraic topology pp. 248--258 Universidad Nacional Autsnoma de Mixico and UNESCO, Mexico City 21 #2234 SPANIER, E. H. Duality and the suspension category. 1958 Symposium internacional de topologma algebraica International symposi um on algebraic topology pp. 259--272 Universidad Nacional Autsnoma de Mixico and UNESCO, Mexico City 21 #2236 VAN EST, W. T. A generalization of the Cartan-Leray spectral sequence. I, II. Nederl. Akad. Wetensch. Proc. Ser. A 61 = Indag. Math. 20 1958 399--413. 21 #2680a BOCKSTEIN, MEYER. Sur le spectre d'homologie d'un complexe. (French) C. R. Acad. Sci. Paris 247 1958 259--261. 21 #2680b BOCKSTEIN, MEYER. Sur la formule des coefficients universels pour les groupes d'homologie. (French) C. R. Acad. Sci. Paris 247 1958 396--398. 21 #2980 HU, SZE-TSEN. Algebraic local invariants of topological spaces. Compositio Math. 13 1958 173--218 (1958). 21 #3471 NAKAYAMA, TADASI. On algebras with complete homology. Abh. Math. Sem. Univ. Hamburg 22 1958 300--307. 21 #3838 DARBO, GABRIELE. Teoria dell'omologia in una categoria di mappe plurivalenti ponderate. (Italian) Rend. Sem. Mat. Univ. Padova 28 1958 188--220. 21 #3850 SPANIER, E. H.; WHITEHEAD, J. H. C. Duality in relative homotopy theory. Ann. of Math. (2) 67 1958 203--238. 21 #4176 ROSENBERG, ALEX; ZELINSKY, DANIEL. Finiteness of the injective hull. Math. Z. 70 1958/1959 372--380. 21 #4421 SCHUBERT, HORST. Semisimpliziale Komplexe. (German) Jber. Deutsch. Math. Verein 61 1958 Abt. 1, 126--138. 21 #4960 LANG, SERGE; TATE, JOHN. Principal homogeneous spaces over abelian varieties. Amer. J. Math. 80 1958 659--684. 21 #5189 ECKMANN, BENO. Groupes d'homotopie et dualiti. (French) Bull. Soc. Math. France 86 1958 271--281. 21 #5196 POENARU, VALENTIN. Considirations sur les variitis simplement connexes ` $3$ dimensions. (French) Rev. Math. Pures Appl. 3 1958 139--156. 21 #5668 NAKAYAMA, TADASI. Note on fundamental exact sequences in homology and cohomology for non-normal subgroups. Proc. Japan Acad. 34 1958 661--663. 22 #1898 KAN, DANIEL M. On homotopy theory and c.s.s. groups. Ann. of Math. (2) 68 1958 38--53. 22 #1899 KAN, DANIEL M. An axiomatization of the homotopy groups. Illinois J. Math. 2 1958 548--566. 22 #1900 KAN, DANIEL M. On monoids and their dual. Bol. Soc. Mat. Mexicana (2) 3 1958 52--61. 22 #61 BERSTEIN, I. Geometric dimension of abelian groups. (Russian) Rev. Math. Pures Appl. 3 1958 93--99. 22 #6817 BOREL, ARMAND; SERRE, JEAN-PIERRE. Le thiorhme de Riemann-Roch. (French) Bull. Soc. Math. France 86 1958 97--136. 22 #6818 GROTHENDIECK, ALEXANDER. La thiorie des classes de Chern. (French) Bull. Soc. Math. France 86 1958 137--154. 22 #6835 KUNIYOSHI, HIDEO. Cohomology theory and different. Tthoku Math. J. (2) 10 1958 313--337. 22 #6836 KUNIYOSHI, HIDEO. On the cohomology groups of ${.germ p}$-adic number fields. Proc. Japan Acad. 34 1958 609--611. 22 #12509 GLEASON, ANDREW M. Projective topological spaces. Illinois J. Math. 2 1958 482--489. 23 #A3569 KAN, DANIEL M. Minimal free c.s.s. groups. Illinois J. Math. 2 1958 537--547. 24 #A1301 KAN, DANIEL M. Adjoint functors. Trans. Amer. Math. Soc. 87 1958 294--329. 24 #A1720 KAN, DANIEL M. Functors involving c.s.s. complexes. Trans. Amer. Math. Soc. 87 1958 330--346. 24 #B416 ROSEN, ROBERT. The representation of biological systems for the stand-point of the theory of categories. Bull. Math. Biophys. 20 1958 317--342. 27 #4851 HEATON, R.; WHAPLES, G. Polynomial cocycles. Duke Math. J. 25 1958 691--696. 31 #233 YONEDA, NOBUO. Note on products in ${.rm Ext}$. Proc. Amer. Math. Soc. 9 1958 873--875. 1942 1 1945 1 1947 1 1948 3 1951 2 1952 1 1953 3 1954 3 1955 6 1956 14 1957 36 1958 72 ********************************************************************** 4,134d 20.0X Eilenberg, Samuel; Mac Lane, Saunders Natural isomorphisms in group theory. Proc. Nat. Acad. Sci. U. S. A. 28, (1942). 537--543. A vague idea of covariance and contravariance is often met with in group-theory, topology, etc.; that is, one feels that the character- group is contravariant to the group, that the homology and co-homology groups of a complex are, respectively, covariant and contravariant to the complex. This is of special importance in the building up of limits of direct and inverse systems ("projective" and "inductive" limits) of groups, spaces, etc. The authors have succeeded in finding for this a precise definition, which is likely to be helpful in classifying and systematizing known results and also in looking for new relations between groups. In this note, they give a brief sketch of their method, for groups only. The main idea is that of a functor, which will best be explained by an example: for them, the definition of the character-group to an Abelian group $G$ is only one half of the definition of a functor, which they call $Ch (G)$, the other half being the (obvious) rule by which any homomorphism of $G$ into another group $H$ determines a homomorphism of the character-group of $H$ into the character-group of $G$. Generally speaking, a functor, associated with some groups $G\*sb 1,G\sb 2,\cdots$, consists of the definition of some associated group, together with a rule indicating that the latter behaves in a certain prescribed fashion under homomorphic transformations affecting $G\sb 1,G\sb 2,\cdots$. Examples are given to illustrate this concept; in particular, the authors use it to derive some interesting relations concerning Whitney's "tensor- product" of groups, and clarify the nature of the latter. Reviewed by A. Weil 9,297h 56.0X Hu, Sze-tsen An exposition of the relative homotopy theory. Duke Math. J. 14, (1947). 991--1033. Although a large amount of knowledge has accumulated about the homotopy groups of Hurewicz, this is the first organized account of the topic. Both the absolute and relative homotopy groups are defined and their basic group properties established. The "homotopy sequence" of a pair $(Y,Y\sb 0)$ is proved to be exact, and is shown to be a covariant functor under mappings. The operations of $\pi\sp 1(Y\sb 0)$ on $\pi\sp n(Y,Y\sb 0)$ are defined and the question of simplicity is studied. The Hurewicz theorem is proved in the relative case: $\pi\sp n(Y,Y\sb 0)\approx H\sp n(Y,Y\sb 0)$ if $(Y,Y\sb 0)$ is $r$-aspherical for $r Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Ofji-00016S-00 for categories-list@mta.ca; Thu, 10 Jan 2002 09:59:19 -0400 Message-Id: To: categories-list@mta.ca Subject: categories: ICALP Extended deadline From: icalp2002@informatica.uma.es To: categories@mta.ca Message-Id: Date: Wed, 09 Jan 2002 13:45:47 +0100 Sender: cat-dist@mta.ca Precedence: bulk We apologize for possible multiple postings. One week extension of paper submission deadline and invited speakers ------------------------------------------------------------------------- Within the last two weeks the conference chairs have received multiple requests to extend the paper submission deadline. In response to it, the submission deadline for papers is extended for a week (until 23:59:59 GMT of 21th January). Note that we will not be able to extend this=20 deadline any further. The complete list of invited speakers is as follows: Manuel Hermenegildo Heikki Mannila Madhav Marathe Andrew Pitts John Reif The 2002 G=F6del Prize and The 2002 EATCS Prize: Maurice Nivat For information about the conference visit the web page: http://www.lcc.uma.es/ICALP2002 Best Regards, 10-Jan-2002 10:02:09 -0400,1801;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:09 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16OflC-0001OK-00 for categories-list@mta.ca; Thu, 10 Jan 2002 10:00:50 -0400 Date: Wed, 9 Jan 2002 10:40:52 -0500 (EST) From: F W Lawvere Reply-To: wlawvere@acsu.buffalo.edu To: categories@mta.ca Subject: categories: Re: categorical incunabula In-Reply-To: <200201081338.g08Dc5h00906@saul.cis.upenn.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk This summary of that exciting epoch will be useful. A crucial omission is the Eilenberg-Zilber 1950 paper in the Annals (reviewed by H. Cartan). This introduction of the category now called simplicial sets was quite crucial in the development of category theory and its applications, for example the 1949 application by Eilenberg and Mac Lane in their discovery of the k-invariants. The first lines of the paper emphasize that the points functor is not faithful . I like to cite this category when confronted by recalcitrant logicians or "universal topologists" who insist that such categories are "abstract"; " real mathematicians" have been using them routinely for over fifty years. ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************ 10-Jan-2002 10:02:13 -0400,2242;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:13 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Ofik-0001F7-00 for categories-list@mta.ca; Thu, 10 Jan 2002 09:58:18 -0400 Message-ID: From: S.J.Vickers@open.ac.uk To: categories@mta.ca Subject: categories: RE: Categories and cognition Date: Wed, 9 Jan 2002 10:11:42 -0000 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2653.19) Content-Type: text/plain; charset="iso-8859-1" Sender: cat-dist@mta.ca Precedence: bulk Posina Venkata Rayudu wrote: > Pictures, by themselves, don't support propositions > that take yes-or-no truth-values. A string (a > concatenation) of images cannot replace well-formed > formulae, assertion. > > I dare not speculate as to whether non-Boolean > truth-value object of topos has any bearing on > Wittgenstein's 'proof against pictures in thinking.' I would say this. It is often useful to work in the so-called geometric logic: not the full intuitionistic internal logic of toposes but that fragment of it that is stable under pullback along geometric morphisms. For instance, it is closely related to continuity, and reasoning geometrically can give automatic continuity proofs. Geometric logic does not have negation as a logical connective, and consequently you approach a proposition asking not "Is this true or false?", but "What truth do I find in this?" (A concrete example is a computer program that is taking a long time to complete. It may have gone into an infinite loop, but you will never discover this. The question "Does this terminate or not?" is not the useful one in practice; instead you ask "Have I got a result yet?") Somehow (and I don't think I can be any less vague here) this approach to truth feels a more appropriate one for visual imagery, and even for much verbal imagery, such as that of poetry, philosophy or religion. Is the story of the Good Samaritan true or false? Quite probably false: it never happened exactly as stated. But that misses the point that you can still find truth in it. Steve Vickers. 10-Jan-2002 10:02:16 -0400,822;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Ofhx-0000ss-00 for categories-list@mta.ca; Thu, 10 Jan 2002 09:57:29 -0400 Date: Wed, 9 Jan 2002 02:41:29 -0500 (EST) From: Peter Freyd Message-Id: <200201090741.g097fTo10273@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Re: lluf subcategory Sender: cat-dist@mta.ca Precedence: bulk Paul writes: I've heard the term "lluf subcategory" meaning "subcategory with the same objects but possibly fewer morphisms". Is there a reference for this usage? I think I have to plead guilty for this. But I don't know where the crime was first committed in print. 10-Jan-2002 10:02:19 -0400,1048;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16OfgZ-000127-00 for categories-list@mta.ca; Thu, 10 Jan 2002 09:56:03 -0400 Date: Tue, 8 Jan 2002 23:14:42 +0000 (GMT) From: Andrew Ker To: categories@mta.ca Subject: categories: Re: lluf subcategory In-Reply-To: <200201081209.g08C92s04355@foobar.pps.jussieu.fr> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk > I've heard the term "lluf subcategory" meaning "subcategory with the > same objects but possibly fewer morphisms". Is there a reference for > this usage? I read it in Crole's "Categories for Types", page 49. Andrew ...... Andrew.Ker@comlab.ox.ac.uk ...... Junior Research Fellow ...... University College, Oxford, OX1 4BH ...... Tel: +44 1865 276618 10-Jan-2002 10:02:22 -0400,4896;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:22 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16OfhJ-0000Dq-00 for categories-list@mta.ca; Thu, 10 Jan 2002 09:56:49 -0400 Date: Tue, 8 Jan 2002 23:07:22 -0500 (EST) From: larry moss To: cmcs@cs.indiana.edu Subject: categories: CMCS 02 2nd Call For Papers (extended deadline) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk [Apologies for multiple copies] FINAL CALL FOR PAPERS CMCS2002 Deadline: January 18, 2002 5th International Workshop on Coalgebraic Methods in Computer Science Grenoble, France 6-7 April 2002 A satellite workshop of ETAPS 2002 Aims and Scope -------------- During the last few years, it is becoming increasingly clear that a great variety of state-based dynamical systems, like transition systems, automata, process calculi and class-based systems can be captured uniformly as coalgebras. Coalgebra is developing into a field of its own interest presenting a deep mathematical foundation, a growing field of applications and interactions with various other fields such as reactive and interactive system theory, object oriented and concurrent programming, formal system specification, modal logic, dynamical systems, control systems, category theory, algebra, analysis, etc. The aim of the workshop is to bring together researchers with a common interest in the theory of coalgebras and its applications. The topics of the workshop include, but are not limited to: the theory of coalgebras (including set theoretic and categorical approaches); coalgebras as computational and semantical models (for programming languages, dynamical systems, etc.); coalgebras in (functional, object-oriented, concurrent) programming; coalgebras and data types; (coinductive) definition and proof principles for coalgebras (with bisimulations or invariants); coalgebras and algebras; coalgebraic specification and verification; coalgebras and (modal) logic; coalgebra and control theory (notably of discrete event and hybrid systems). The workshop will provide an opportunity to present recent and ongoing work, to meet colleagues, and to discuss new ideas and future trends. Previous workshops of the same series have been organized in Lisbon, Amsterdam, Berlin, and Genova. The proceedings appeared as Electronic Notes in Theoretical Computer Science (ENTCS) Volumes 11,19, 33, and 41. You can get an idea of the types of papers presented at the meeting by looking at the tables of contents of the ENTCS volumes from the meetings, available at the ENTCS page. For venue, registration and suggested accommodation see the ETAPS2002 web page, http://www-etaps.imag.fr/ Submissions ----------- Submissions will be evaluated by the Program Committee for inclusion in the proceedings, which will be published in the ENTCS series. Papers must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Papers (of at most 15 pages) should be submitted electronically as uuencoded PostScript files at the address cmcs@cs.indiana.edu. A separate message should also be sent, with a text-only one-page abstract and with mailing addresses (both postal and electronic), telephone number and fax number of the corresponding author. Important Dates ---------------- Deadline for submission: 18 January 2002. Thanks to all who submitted papers already. Notification of acceptance: 20 February 2002. Final version due: 10 March 2002. Workshop dates: 6-7 April 2002. Invited Speakers ---------------- Our list of invited speakers is coming, and will be announced on the web page for the conference, http://www.cs.indiana.edu/cmcs/ Program Committee ------------------- J. Adamek (Braunschweig) Alexandru Baltag (Amsterdam) Jesse Hughes (Nijmegen) H. Peter Gumm (Marburg) Alexander Kurz (Amsterdam) Bart Jacobs (Nijmegen) Marina Lenisa (Udine) Ugo Montanari (Pisa) Larry Moss (chair, Bloomington, IN) Ataru T. Nakagawa (Tokyo) John Power (Edinburgh) Horst Reichel (Dresden) Jan Rutten (Amsterdam) For more information --------------------- http://www.cs.indiana.edu/cmcs/ cmcs@cs.indiana.edu 10-Jan-2002 10:02:25 -0400,1284;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 10:02:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16OfkK-00019L-00 for categories-list@mta.ca; Thu, 10 Jan 2002 09:59:56 -0400 Date: Wed, 9 Jan 2002 15:34:51 +0100 (MET) From: Jiri Adamek X-Sender: adamek@lisa To: categories Subject: categories: effective topos Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk In the study of iterative theories we use the concept of a strongly locally presentable category. This is an extensive, locally finitely presentable category such that a. hom-sets of finitely presentable objects are finite and b. a strong quitent of a finitely presentable object is finitely pres. I would appreaciate knowing whether the effective topos has all these properties. Thanks, Jiri Adamek xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 10-Jan-2002 22:33:44 -0400,1768;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 22:33:44 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16OrR6-0006YR-00 for categories-list@mta.ca; Thu, 10 Jan 2002 22:28:52 -0400 Message-ID: <3C3D6FA1.C77AE0BA@actcom.co.il> Date: Thu, 10 Jan 2002 12:40:33 +0200 From: Zippora Arzi-Gonczarowski X-Mailer: Mozilla 4.73 [en] (Win95; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca, levy@pps.jusieu.fr Subject: categories: Re: lluf subcategory References: <200201081209.g08C92s04355@foobar.pps.jussieu.fr> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Hi, Paul LEVY wrote: > I've heard the term "lluf subcategory" meaning "subcategory with > the same objects but possibly fewer morphisms". Is there a > reference for this usage? Two references to "lluf subcategories" that I am aware of: 1. Categories for Types - Roy L. Crole - 1993 - page 49 2. Practical Foundations of Mathematics - Paul Taylor - 1999 - page 211 (where the term "wide subcategory" is suggested as synonym). And thank you, Paul, for bringing this up, since it reminded me to ask: Does anyone know the origin of the term "lluf", or how it should be pronounced? Zippie -- --------------------------------------------------------------------- Dr. Zippora Arzi-Gonczarowski Typographics, Ltd. 46 Hehalutz St. Jerusalem 96222, Israel URL - http://www.actcom.co.il/typographics/zippie E-mail - zippie@actcom.co.il Tel: (+972)-2-6437819 Fax: (+972)-2-6434252 --------------------------------------------------------------------- 10-Jan-2002 22:40:05 -0400,1283;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 22:40:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Orbj-0006ym-00 for categories-list@mta.ca; Thu, 10 Jan 2002 22:39:51 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 10 Jan 2002 16:28:00 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: lluf subcategory In-Reply-To: <200201090741.g097fTo10273@saul.cis.upenn.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Charles found the phrase "wide subcategory" and it appears that way in CTCS. Much preferred IMHO. But chacun a son (de)gout. On Wed, 9 Jan 2002, Peter Freyd wrote: > Paul writes: > > I've heard the term "lluf subcategory" meaning "subcategory with the > same objects but possibly fewer morphisms". Is there a reference > for this usage? > > I think I have to plead guilty for this. But I don't know where > the crime was first committed in print. > > > > 10-Jan-2002 22:41:20 -0400,4643;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 10 Jan 2002 22:41:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Orcw-0007F5-00 for categories-list@mta.ca; Thu, 10 Jan 2002 22:41:06 -0400 Date: Thu, 10 Jan 2002 13:13:51 -0500 (EST) From: F W Lawvere Reply-To: wlawvere@acsu.buffalo.edu To: categories Subject: categories: Re: effective topos In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Dear Jirka, My partial understanding of the effective topos suggests that it is not LFP and indeed does not even have small colimits. It is not a Grothendieck topos (i.e. does not have a geometric morphism to sets with a discrete left adjoint, although it does misleadingly have a "codiscrete"-like functor from sets). Replying to your two specific questions: a) The effective topos does not have many finite hom sets, as can be seen by comparing it with the approximation below. b) In the absence of colimits, it is not clear how to even formulate the idea that finite generation implies finite presentability. There is a first approximation, due to Phil Mulry, which is a categorical version of the concepts of Banach, Mazur, and Ersov. It is not only a topos, but a Grothedieck topos and indeed a coherent one and hence locally finitely presentable. Consider the category of recursive sets and recursive maps (or equivalently just the monoid of recursive endomaps of N). Its canonical Grothendieck topology turns out to be finitary. The Mulry topos consists of sheaves on this site. In a sense, all maps and objects have some aspect of recursiveness or "effectiveness" in the spirit of Banach, Mazur, and Ersov, and the distinction between "recursive" and "recursively enumerable" does not apply to objects, but rather to inclusion maps, which may or may not have Boolean complements. Perhaps though, as you suggest, a category generated by a category with finite hom sets would better express the needs of iteration theory than anything (like the effective topos) based on an already-achieved bad infinity. There is an issue involving recursivity that categorists should settle: How general is Higman's theorem? In group theory the word problem (whether a given finitely generated group is recursively related) is equivalent to the purely algebraic one of whether the given group can be embedded as a subgroup of a finitely presentable one. For which other algebraic categories is the same statement true? or is it possibly true for the category of single-sorted algebraic theories? The latter problem was posed by Bill Boone, but as far as I know, is not yet resolved. For the category of first-order theories, a theorem analogous to Higman's was proved by Craig and Vaught; for that case, they gave a kind of intuitive argument: using a few additional predicates one can express enough of number theory to encode a fragmentary satisfaction relation and any given recursive set of axioms, so that one can then add the one additional axiom that says "all those axioms are true". Of course, it is non-trivial that this argument actually works. Do you or anybody on the catnet know of any progress on this question? Bill ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************ On Wed, 9 Jan 2002, Jiri Adamek wrote: > In the study of iterative theories we use the concept of a strongly > locally presentable category. This is an extensive, locally finitely > presentable category such that > a. hom-sets of finitely presentable objects are finite > and > b. a strong quitent of a finitely presentable object is finitely pres. > I would appreaciate knowing whether the effective topos has all these > properties. > Thanks, > Jiri Adamek > > > xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx > alternative e-mail address (in case reply key does not work): > J.Adamek@tu-bs.de > xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx > > > > > > 11-Jan-2002 08:50:59 -0400,3619;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 11 Jan 2002 08:50:59 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16P16z-0007Qr-00 for categories-list@mta.ca; Fri, 11 Jan 2002 08:48:45 -0400 Message-ID: <018101c19a4b$360f1f70$0100a8c0@farmer> Reply-To: "Michael Mislove" From: "Michael Mislove" To: Subject: categories: Clifford Lectures and MFPS XVIII Date: Thu, 10 Jan 2002 20:53:55 -0600 Organization: Tulane University MIME-Version: 1.0 X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Sender: cat-dist@mta.ca Precedence: bulk Apologies for Multiple Notices! Dear Colleagues, This is the Second Announcement and Call for Participation for two events. The first is the 2002 Clifford Lectures, which will take place on the campus of Tulane University, New Orleans, LA USA from the afternoon of March 20, 2002 through the morning of March 23, 2002. This annual series of lectures is sponsored by the Tulane Mathematics Department, and this year's lecturer is Sergei N. Artemov (CUNY Graduate Center). Professor Artemov will deliver three lectures, and there also will be lectures by Samson Abramsky, Henk Barendregt, Samuel Buss, Nachum Derschowitz, Yuri Gurevich, Joshua Guttman, Juris Hartmanis, Dexter Kozen, Rohit Parikh, Helmut Schwichtenberg and Moshe Vardi. More information can be found at http://www.math.tulane.edu/~mfps/clifford.html A program will be posted there when details are available. The second event is the Eighteenth Workshop in the Mathematical Foundations of Programming Semantics, MFPS XVIII. This event also will be held at Tulane, and it will begin on the afternoon of Saturday, March 23 and run through Tuesday, March 26. This year's meeting will feature invited talks by Rajeev Alur, Patrick Cousot, John Hatcliff, John Mitchell, John Reynolds and Doug Smith, as well as four special sessions. In addition, contributed talks from participants are invited - available slots will be allocated on a first come, first served basis. More information about the meeting - including a detailed list of the special sessions, can be found at the URL http://www.math.tulane.edu/~mfps/mfps18.html A program will be posted when details are available. We have some limited support available for women, minorities and graduate students who wish to attend either meeting. These funds are provided by the ONR, and we anticiapte some additional limited funding from the NSF. Participants can register online for either one or both of these meetings by going to the URL https://math.tulane.edu/~mfps/registration The registration form allows participants to reserve hotel rooms, and also to submit a title and short abstract for a proposed contriibuted talk at MFPS. Hotel arrangements for the meetings are at a reduced rate, and the block of rooms has been reserved only until February 13, 2002. After that date, there is no guarantee that rooms will be available, and those that are available will be at a substantially higher cost. Best regards, Mike Mislove Michael W. Mislove =20 Professor and Chairman Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University Email: mwm@math.tulane.edu New Orleans, LA 70118 URL: http://www.math.tulane.edu/~mwm USA 11-Jan-2002 08:51:02 -0400,1805;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 11 Jan 2002 08:51:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16P183-0007SM-00 for categories-list@mta.ca; Fri, 11 Jan 2002 08:49:51 -0400 Date: Fri, 11 Jan 2002 12:05:29 +0100 (CET) From: Message-Id: <200201111105.MAA02026@kodder.math.uu.nl> To: categories@mta.ca Subject: categories: effective topos Cc: jvoosten@math.uu.nl X-Sun-Charset: US-ASCII X-Virus-Scanned: by AMaViS snapshot-20010407 Sender: cat-dist@mta.ca Precedence: bulk Dear all, As Thomas and Bill pointed out, the effective topos is quite far from being cocomplete; indeed, a countable coproduct of copies of 1 does not exist. So the locally finitely presentable machinery seems not to work here, at least, externally. Bill points to Mulry's recursive topos as an approximation. Here is a question, related to a possible other approximation. Does the effective topos have a dense set of generators? In this case one could embed it into a Grothendieck topos by an embedding which preserves a lot of structure. It is easy to see that the full subcategory of Eff on the countable projective objects is essentially small and generates Eff. But is it dense? This is related to the following question: does the functor Nabla: Sets --> Eff preserve \omega _1-filtered colimits? (it is easy to see that it doesn't preserve filtered colimits; it does preserve \omega _1-filtered colimits as functor from Sets to the separated objects of Eff) I have been trying for some time to solve this; but I couldn't. It appears that set-theoretic combinatorics plays an important role here, and is more important than recursiveness. Jaap van Oosten 11-Jan-2002 08:51:05 -0400,2228;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 11 Jan 2002 08:51:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16P18h-0007VM-00 for categories-list@mta.ca; Fri, 11 Jan 2002 08:50:31 -0400 Date: Fri, 11 Jan 2002 11:47:42 +0000 (GMT) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: Re: lluf subcategory In-Reply-To: <3C3D6FA1.C77AE0BA@actcom.co.il> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *16P09x-0004a5-00*KHEo5CmILyU* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk > > > I've heard the term "lluf subcategory" meaning "subcategory with > > the same objects but possibly fewer morphisms". Is there a > > reference for this usage? > > Two references to "lluf subcategories" that I am aware of: > > 1. Categories for Types - Roy L. Crole - 1993 - page 49 > > 2. Practical Foundations of Mathematics - Paul Taylor - 1999 - page 211 > (where the term "wide subcategory" is suggested as synonym). > > And thank you, Paul, for bringing this up, since it reminded me to ask: > > Does anyone know the origin of the term "lluf", or how it should be > pronounced? > I've been looking through Peter Freyd's papers, and the earliest occurrence of "lluf" that I can find is in "Algebraically complete categories", published in the proceedings of the 1990 Como meeting (Springer LNM 1488, 1991). It is used there (on page 101) without comment or explanation, which suggests that Peter must have used it before, but I can't find an earlier occurrence. A lower bound for its first occurrence is provided by Peter's paper "Choice and well-ordering" (Ann. Pure Appl. Logic 35, 1987), where the concept occurs without being so named. As regards pronunciation, I've always thought that since it looks like a Welsh word it should be pronounced as such, i.e. (approximately) "thleeve". (The Welsh "ll" doesn't correspond to any sound representable by a combination of consonants in English.) Peter Johnstone 11-Jan-2002 08:51:08 -0400,743;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 11 Jan 2002 08:51:08 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16P19A-0007Uf-00 for categories-list@mta.ca; Fri, 11 Jan 2002 08:51:00 -0400 Date: Fri, 11 Jan 2002 07:14:58 -0500 (EST) From: Peter Freyd Message-Id: <200201111214.g0BCEwC15439@saul.cis.upenn.edu> To: categories@mta.ca, levy@pps.jusieu.fr, zippie@actcom.co.il Subject: categories: Re: lluf subcategory Sender: cat-dist@mta.ca Precedence: bulk Zippie asks: Does anyone know the origin of the term "lluf", or how it should be pronounced? Pronounce it by pronouncing the word "full" only backwards. 11-Jan-2002 12:19:21 -0400,1787;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 11 Jan 2002 12:19:21 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16P4JQ-0001SM-00 for categories-list@mta.ca; Fri, 11 Jan 2002 12:13:49 -0400 Message-Id: <5.1.0.14.2.20020111090239.024229d0@mail.oberlin.net> X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Fri, 11 Jan 2002 09:16:35 -0500 To: categories@mta.ca From: Charles Wells Subject: categories: lluf Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk "Lluf" is "full" written backward. Full means if the subcategory has two objects it has all the arrows between them. Lluf means the subcategory has all the objects of the containing category but not necessary all the arrows. Lluf is not a categorical notion. The more useful notion is REPRESENTATIVE subcategory. D is a representative subcategory of C if every object of C is isomorphic to an object of D. I think some writers have used "extensive" for "representative" but I don't have a reference. I don't know the history of those words. Charles Wells, Emeritus Professor of Mathematics, Case Western Reserve University Affiliate Scholar, Oberlin College Send all mail to: 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html genealogical website: http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm 12-Jan-2002 09:09:03 -0400,2950;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 12 Jan 2002 09:09:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16PNrK-0008I4-00 for categories-list@mta.ca; Sat, 12 Jan 2002 09:06:06 -0400 To: categories@mta.ca Subject: categories: Enriched category theory, again From: Mark Hovey Date: 12 Jan 2002 05:40:38 -0500 Message-ID: Lines: 40 User-Agent: Gnus/5.070095 (Pterodactyl Gnus v0.95) Emacs/20.3 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk I am back again, with two more questions about enriched category theory. As usual, what I am really searching for are references so I can avoid writing any category-theoretic proofs myself. The good news is that Max Kelly's book on enriched category theory is actually making sense to me now (thank you, Max!). I think these two questions are not answered in there, but I could be wrong. The first is a generalization of the enriched Yoneda lemma. Recall that this says that [A,V](X^*,F) is isomorphic to FX. Here [A,V] denotes the V-category of V-functors from A to V, X is an object of A, and X^* is the V-functor that takes Y to A(X,Y). (and A is small). What I want is [A,D](Y tensor X^*,F) is isomorphic to D(Y,FX). Here D is a V-category that is tensored over V, X is an object of A, and Y is an object of D. The functor Y tensor X^* takes Z to Y tensor A(X,Z). If you take D = V and Y = the unit of V, you recover the Yoneda lemma above. I don't remember if any completeness or cocompleteness assumptions on D are necessary here because I always assume D is bicomplete. Has this stonger Yoneda lemma appeared in print anywhere? I think the proof is the same as the usual Yoneda lemma. My second question has to do with Brian Day's old work. He shows that if A is a small symmetric monoidal V-category, then [A,V] is a closed symmetric monoidal V-category. What I want to say is that if D is a (bicomplete) V-category that is tensored and cotensored over V, then [A,D] is an [A,V]-category that is tensored and cotensored over [A,V] (A is as above, a small symmetric monoidal V-category). This is obviously a generalization of Day's work, and is obviously proved by following along in Day and changing a few V's to D's. Has it ever appeared in print? What I am actually doing (with Manos Lydakis), in case anyone is wondering why I am asking all these questions, is examining the homotopy theory of [A,D]. So I assume V and D are themselves model categories and put different model structures on [A,D]. For certain A you recover what algebraic topologists call spectra and symmetric spectra. The main goal is to explain and generalize the Goodwillie calculus of functors. Mark Hovey 12-Jan-2002 09:09:20 -0400,2877;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 12 Jan 2002 09:09:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16PNuD-0008OE-00 for categories-list@mta.ca; Sat, 12 Jan 2002 09:09:05 -0400 Message-ID: <3C3F1639.4B1AEDC2@bangor.ac.uk> Date: Fri, 11 Jan 2002 16:43:37 +0000 From: Ronnie Brown X-Mailer: Mozilla 4.79 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: lluf References: <5.1.0.14.2.20020111090239.024229d0@mail.oberlin.net> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk The term commonly used for the corresponding concept to lluf for groupoids is `wide'. I won't give a preference! `Representative subgroupoid' is used as for categories. Both occur in my 1968 book on topology, and I seem to remember the term wide was new. Ronnie Brown Charles Wells wrote: > > "Lluf" is "full" written backward. Full means if the subcategory has two > objects it has all the arrows between them. Lluf means the subcategory has > all the objects of the containing category but not necessary all the > arrows. Lluf is not a categorical notion. The more useful notion is > REPRESENTATIVE subcategory. D is a representative subcategory of C if > every object of C is isomorphic to an object of D. I think some writers > have used "extensive" for "representative" but I don't have a reference. I > don't know the history of those words. > > Charles Wells, > Emeritus Professor of Mathematics, Case Western Reserve University > Affiliate Scholar, Oberlin College > Send all mail to: > 105 South Cedar St., Oberlin, Ohio 44074, USA. > email: charles@freude.com. > home phone: 440 774 1926. > professional website: http://www.cwru.edu/artsci/math/wells/home.html > personal website: http://www.oberlin.net/~cwells/index.html > genealogical website: > http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ > NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm -- Professor Emeritus R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Raising Public Awareness of Mathematics CDRom Version 1.1 http://www.bangor.ac.uk/~mas010/CDadvert.html Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/ 12-Jan-2002 09:15:25 -0400,2707;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 12 Jan 2002 09:15:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16PO08-0008Q2-00 for categories-list@mta.ca; Sat, 12 Jan 2002 09:15:12 -0400 Message-Id: <5.1.0.14.1.20020109190927.009f84b0@mailx.u-picardie.fr> X-Sender: ehres@mailx.u-picardie.fr X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Thu, 10 Jan 2002 17:30:55 +0100 To: categories@mta.ca From: Andree Ehresmann Subject: categories: Re: categorical incunabula In-Reply-To: <200201081338.g08Dc5h00906@saul.cis.upenn.edu> Mime-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk The list of MathSciNet publications that mention categories or functors established by Peter Freyd is most interesting. May I point to 2 important papers by Charles Ehresmann in this period which, though not using the word "category", might also be relevant since they extensively use "groupoids" (i.e., categories in which all the morphisms are invertible) and are at the root of a large part of the subsequent work on categories done by and around Charles in the sixties? I don't have access to the MathSciNet reference, but it should be easy to find. 1. Les prolongements d'une variete differentiable, Atti IV Congresso Unione Matematica Italiana, Taormina (1951), 1-9. In this paper Charles defines what will be later called "the category of infinitesimal jets" (between differentiable manifolds), with its domain, codomain and composition maps, but without using the name category (he said to me that he did not know of categories at this date). And he explicitly mentions that the invertible jets form a groupoid. 2. Les prolongements d'un espace fibre differentiable, C.R.A.S. Paris, 240(1955 ), 1755-1757. Here Charles defines the action of a groupoid on a set and its associated "principal groupoid" as a generalization of the fibre bundle theory. he had developed in the fourties. He also considers the topological and differentiable cases, thus giving the first definition of an "internal" groupoid and groupoid action. He applies this to study the prolongations of manifolds. His 1957 paper on categories (cited in the list) is a direct sequel of this paper, except that the groupoids are then replaced by categories. And the internal case has led in 1963 to his extensive study of internal categories and category actions (he used then the term "structured" instead of "internal"). With my best wishes for all Andree C. Ehresmann 13-Jan-2002 19:35:24 -0400,3660;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 13 Jan 2002 19:35:24 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Pu0w-0001Ay-00 for categories-list@mta.ca; Sun, 13 Jan 2002 19:26:10 -0400 Date: Sun, 13 Jan 2002 16:21:15 -0400 (AST) From: Bob Rosebrugh To: categories Subject: categories: TAC Contents: Volume 8 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Here is the table of contents of Volume 8 and subscription information for the journal Theory and Applications of Categories. The Editors invite high quality submissions. The full table of contents is at www.tac.mta.ca/tac/ THEORY AND APPLICATIONS OF CATEGORIES ISSN 1201-561X Volume 8 - 2001 1. $n$-Permutable locally finitely presentable categories Marino Gran and Maria-Cristina Pedicchio, 1-15 2. Exponentiable Morphisms: posets, spaces, locales, and Grothendieck toposes Susan Niefield, 16-32 3. On sifted colimits and generalized varieties J. Adamek and J. Rosicky, 33-53 4. On Mackey topologies in topological abelian groups Michael Barr and Heinrich Kleisli, 54-62 5. Finite sum - product logic J.R.B. Cockett and R.A.G. Seely, 63-99 6. On the pullback stability of a quotient map with respect to a closure operator Lurdes Sousa, 100-113 7. Duality for simple $\omega$-categories and disks Mihaly Makkai and Marek Zawadowski, 114-243 8. Finite sets and symmetric simplicial sets Marco Grandis, 244-252 9. How algebraic is algebra? J. Adamek, F. W. Lawvere and J. Rosicky, 253-283 10. Localization of $V$-categories Bjorn Ian Dundas, 284-312 11. Limites inductives point par point dans les catgories accessibles Pierre Ageron, 313-323 12. Combinatorics of branchings in higher dimensional automata Philippe Gaucher, 324-376 13. How large are left exact functors? J. Adamek, V. Koubek and V. Trnkova, 377-390 14. A categorical genealogy for the congruence distributive property Dominique Bourn, 391-407 15. Pseudogroupoids and commutators George Janelidze and M.Cristina Pedicchio, 408-456 16. Perfect Maps are Exponentiable - Categorically Gunther Richter and Walter Tholen, 457-464 17. Essential localizations and infinitary exact completion Enrico M. Vitale, 465-480 18. Cartesian closed topological hull of the construct of closure spaces V. Claes, E. Lowen-Colebunders and G. Sonck, 481-489 19. A sheaf-theoretic view of loop spaces Mark W. Johnson, 490-508 20. On Functors Which Are Lax Epimorphisms Jiri Adamek, Robert El Bashir, Manuela Sobral, Jiri Velebil, 509-21 21. Closure operators in exact completions Matias Menni, 522-540 22. The extensive completion of a distributive category J.R.B. Cockett and Stephen Lack, 541-554 23. V-Cat is locally presentable or locally bounded if V is so G. M. Kelly and Stephen Lack, 555-575 SUBSCRIPTION/ACCESS TO ARTICLES Subscribers to the journal receive abstracts of accepted papers by electronic mail. Compiled TeX (.dvi), Postscript and PDF files of the full articles are available by Web/ftp. To subscribe, send a request to tac@mta.ca, including your name and a postal address. The journal is free to individuals. 14-Jan-2002 19:18:19 -0400,2044;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 14 Jan 2002 19:18:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16QGJC-0007JE-00 for categories-list@mta.ca; Mon, 14 Jan 2002 19:14:30 -0400 Content-Type: text/plain; charset="iso-8859-1" From: Carsten Butz Reply-To: butz@it-c.dk To: categories@mta.ca Subject: categories: PSSL 76 - First Announcement Date: Mon, 14 Jan 2002 14:54:25 +0100 X-Mailer: KMail [version 1.2] MIME-Version: 1.0 Message-Id: <02011414542506.01769@vip164.it-c.dk> Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk PERIPATETIC SEMINAR ON SHEAVES AND LOGIC (PSSL 76) First Announcement Dear friends and colleagues, The 76th PSSL will be held at the IT-University of Copenhagen over the weekend 2-3 March, 2002. As usual we welcome talks on sheaves, category theory, logic, and related areas such as applications in (theoretical) computer science. As the meeting is informal in nature talks on work in progress are also welcome. A second announcement with details on accommodation and registration will follow soon. Please direct all correspondence to Carsten Butz (butz@it-c.dk). Copenhagen is located on the east coast of the island Sjaelland. Copenhagen Airport (airport code CPH) is a major European airport with direct flights to most larger European cities. From the airport it takes less than 15 minutes by train to reach the centre of the city. Also, there are direct trains to Copenhagen from Sweden and from Germany. Day trains from Germany leave from Hamburg Central Station and take 4 1/2 hours (the trains take the ferry between Puttgarden and Roedby). There are also direct night trains from and to the Ruhrgebiet and southern Germany. Best regards, Lars Birkedal (birkedal@it-c.dk) Carsten Butz (butz@it-c.dk) Thomas Hildebrandt (hilde@it-c.dk) Anders Kock (kock@imf.au.dk, Aarhus University) 14-Jan-2002 19:19:38 -0400,2942;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 14 Jan 2002 19:19:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16QGNp-0007RY-00 for categories-list@mta.ca; Mon, 14 Jan 2002 19:19:18 -0400 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15427.4495.154295.399068@chtapach.loria.fr> Date: Mon, 14 Jan 2002 18:12:47 +0100 (MET) From: Christophe Ringeissen To: categories@mta.ca Subject: categories: AMAST'2002: Last Call For Papers X-Mailer: VM 6.75 under 21.1 (patch 14) "Cuyahoga Valley" XEmacs Lucid Reply-To: Christophe.Ringeissen@loria.fr Sender: cat-dist@mta.ca Precedence: bulk [Apologies for multiple copies] SUBMISSION DEADLINE: FEBRUARY 1, 2002 ************************************* AMAST 2002 CALL FOR PAPERS 9-th International Conference on Algebraic Methodology And Software Technology AMAST 2002, September 9-13, 2002 St. Gilles les Bains, Reunion Island, France * Important Dates: Paper submissions February 1, 2002 Notification of paper acceptance April 27, 2002 Camera ready papers June 1, 2002 AMAST 2002 conference September 9-13, 2002 * Topics: As in previous years, we invite papers reporting original research on setting software technology on a firm mathematical basis. Of particular interest is research on using algebraic, logic, and other formalisms suitable as foundations for software technology, as well as software technologies developed by means of logic and algebraic methodologies. * Submissions: We invite prospective authors to submit electronically previously unpublished papers of high quality. Papers must be no longer than 15 pages (6 pages for system demonstrations) and should be prepared using LaTeX and the LNCS style that can be downloaded from the URL: http://www.springer.de/comp/lncs/authors.html Please send a fully self-contained PostScript file to amast@loria.fr As in the past, the AMAST'2002 proceedings will be published by Springer-Verlag in the Lecture Notes in Computer Science Series. * Program Committee: V.S. Alagar, E. Astesiano, M. Bidoit, D. Bolignano, M. Broy, J. Fiadeiro, B. Fischer, K. Futatsugi, A. Haeberer, N. Halbwachs, A. Haxthausen, D. Hutter, P. Inverardi, B. Jacobs, M. Johnson, H. Kirchner (PC chair), P. Klint, T. Maibaum, Z. Manna, J. Millen, P. Mosses, F. Orejas, R. de Queiroz, T. Rus, C. Ringeissen (PC chair assistant), D. Sannella, P.-Y. Schobbens, G. Scollo, A. Tarlecki, M. Wirsing * Local Organization Chair: Teodor Knapik, Univ. de la Reunion * Further information: For regularly updated details of the conference organization send email to amast@loria.fr or visit the AMAST'2002 web page: http://www.loria.fr/conferences/amast2002 15-Jan-2002 08:46:00 -0400,5616;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 15 Jan 2002 08:46:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16QSns-0007wd-00 for categories-list@mta.ca; Tue, 15 Jan 2002 08:35:00 -0400 X-Originating-IP: [128.205.234.32] From: "F. William Lawvere" To: categories@mta.ca Bcc: Subject: categories: SYNTAX vs SEMANTICS ?? Date: Mon, 14 Jan 2002 20:16:53 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 14 Jan 2002 20:16:54.0423 (UTC) FILETIME=[68C00A70:01C19D38] Sender: cat-dist@mta.ca Precedence: bulk Several have asked whether categorical algebra can clarify the relation between syntax and semantics, two terms often paired in theoretical linguistics. The hope is that, as in previous work, focusing on mathematical experience will give information that can be investigated further and which is more richly detailed than abstract speculation about cognition in general has been able to provide. Whatever serious discussion we can have here will be limited to mathematics in particular, although the mathematics may suggest generalizations to other fields. Semantics has been previously analyzed as the contravariant 2-functor which relates the abstract general and the concrete general aspects of each general concept which is admissible in a given doctrine. In some doctrines semantics has an adjoint, called structure, a paradigmatic example of which is the structure that the system of cohomology operations naturally has. This adjoint does not have much directly to do with syntax, except insofar as the structure of something, being an abstract general, is in need of presentations to permit many kinds of calculation and reasoning about it. The word SYNTAX has the same Greek root has TACTICS . That suggests thinking of syntax as the tactics for manipulating symbols , specifically the symbols involved in presentations of abstract generals. More generally we might also include the word problems associated to individual algebraic categories relative to underlying set functors, but that case of 1-categories is distinct from the 2-categorical case I am emphasizing here. Presentations themselves are often objectified for mathematical study, and in all known cases that involves a choice of a further category with an adjoint pair connecting the latter with the category of objects to be presented. For example, in the doctrine where abstract generals are identified with single-sorted algebraic theories a standard choice is the category of sequences of sets, often called "signatures", with the functor assigning to each theory its sequence of ( )-ary operations; the left adjoint is then determined and hence a monad T on the chosen category. That monad has a crucial further role, in the construction of the third category Pres(T) of presentations wherein the signatures also play a further role as AXIOMS : namely this "syntactical" category has as objects pairs G,R of "signatures" equipped with a pair of maps from R to T(G) . The presentation functor applies the left adjoint, then takes the coequalizer in the first category; this presentation functor might also be considered part of syntax. Even if one considered (as was done for many years) that semantics was really the functor going all the way from syntax to the concrete generals, the fact that it has a preferred factorization would not remain concealed forever from mathematicians: the discovery of groups revealed a rich content beyond permutation symbols, and calculations with characteristic polynomials of linear transformations are clarified by, as well as present, the "abstract" rings whose representations are involved (There is a SLNM by Lambek about Linear Semantics). In these terms the choice of home for the notion "theory" can be clarified . There are apparently FOUR reasonable possibilities : 1) The presentations of abstract generals. This syntactical emphasis was the one most used for many decades by logicians. 2) The abstract generals themselves. This choice, exemplified by the term "algebraic theory", emphasizes that theories should be those objects which play the pivotal role of forming the one category which is functorially linked to both syntax and semantics. (Note that there is usually no way of getting from concrete generals to syntax). 3) The concrete generals themselves. The word "theory" has only occasionally been used in this sense, but note that is philosophically analogous to the use of "homology theory" to signify an objective functor. 4) But when a group theorist refers to "group theory" he does not usually mean either 1) or 2), but more like Presentations of his Concrete General ! For 3) has also an algebraic structure, but in a 2- dimensional sense; specifically, in the doctrine of algebraic theories,etc., the concrete generals all have the natural 2-structure presented by filtered colimits, reflexive coequalizers, and all small limits. Thus we could start with any small family of groups and apply any composite of those operations, apply also any other such composite functor, and compare the results homomorphically. 2-syntax as "theory"? _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx 15-Jan-2002 08:46:03 -0400,1594;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 15 Jan 2002 08:46:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16QSot-0007uw-00 for categories-list@mta.ca; Tue, 15 Jan 2002 08:36:03 -0400 Date: Tue, 15 Jan 2002 14:06:56 +1100 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Message-Id: <200201150306.g0F36uD477753@milan.maths.usyd.edu.au> To: categories@mta.ca Subject: categories: Re: Enriched category theory, again Sender: cat-dist@mta.ca Precedence: bulk This is in reply to the queries in Mark Hovey's letter of 12 Jan, of which I shall try to include a copy below; I am limited by the inadequacies of this home computer. The first isomorphism he asks about, namely (using o for tensor product) [A,D](Y o A(X,-),F] =~ D(Y,FX), may be seen as a simple consequence of the fact that Y o A(X,-) is the left Kan extension of Y : I --> D along X : I --> A, where I is the unit V-category; see formula (4.18) or (4.25) of my book. The second question concerns an easy extension of Brian Day's convolution monoidal structure on a presheaf category. An easy way of seeing the truth of Hovey's observation is to recall that a tensored V-category structure on a (mere) category A corresponds to an _action_ of V on A having an appropriate right adjoint; see [Janelidze and Kelly, TAC 9 (2001), 61 - 91], foot of page 66; but the idea itself is quite old. Now V --> [D,D] easily gives [A,V] --> [[A,D],[A,D]]. Of course there is checking to do. Max Kelly. 15-Jan-2002 08:46:06 -0400,1185;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 15 Jan 2002 08:46:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16QSoK-0007xz-00 for categories-list@mta.ca; Tue, 15 Jan 2002 08:35:28 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Mon, 14 Jan 2002 21:38:24 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Upgrade of TTT Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk We have corrected a few errors in TTT and there is new version that can be found on Charles' home page and at ftp.math.mcgill.ca/pub/barr. Thanks to Francisco Marmelejo, Tom Holroyd and Peter Selinger. Peter is responsible for the most substantive change, having noticed that the proof we gave in Chapter one that monics are pullback-stable is incoherent. We welcome all error notices and will eventually correct them. Michael 16-Jan-2002 17:33:19 -0400,2548;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 16 Jan 2002 17:33:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16QxW6-0007Ii-00 for categories-list@mta.ca; Wed, 16 Jan 2002 17:22:42 -0400 User-Agent: Microsoft-Entourage/9.0.2509 Date: Mon, 14 Jan 2002 09:19:42 +0100 Subject: categories: Re: categorical incunabula From: "Hans-E. Porst" To: Message-ID: In-Reply-To: <200201081338.g08Dc5h00906@saul.cis.upenn.edu> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Concerning Peter Freyd's question > Saunders's 1948 paper (without Sammy) first surprised me 40 years ago. > Buchsbaum in his 1955 paper that introduced abelian categories (under > the name "exact categories") said that he saw no way of defining > infinite products. Which meant that he hadn't seen Saunders's 1948 > paper. Is this the first appearance of universal mapping definitions? one certainly might consider A.A. Markov's definition of a free topological group (in 1945) as an earlier appearance: A. A. Markov: On free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 9 (1945), 3-64 [Amer. Math. Soc. Transl. 30 (1950), 11-88; Reprint: Amer. Math. Soc. Transl. Ser. I, 8 (1962), 195-272.] Note, in this context, also the early apperances of what we now would call "applications (or predecessors) of Freyd's GAFT" (though none of these papers has the notions of category or functor) S. Kakutani: Free topological groups and finite discrete product groups, Proc. Imp. Acad. Tokyo 20 (1944), 595-598 P. Samuel: On universal mappings and free topological groups, Bull. Amer. Math. Soc. 54 (1948), 591-598 In his 1957 paper A. I. Malcev: Free topological algebras, Izv. Akad. Nauk SSSR Ser. Mat. 21 (1957), 171-198 [Amer. Math. Soc. Transl. Ser. II, 17 (1961), 173-200.] Malcev already begins his proof of the existence of a free topological algebra (as a topological subgroup of the corresponding product) with the phrase "In the usual way one can now prove". -- Hans-E. Porst porst@math.uni-bremen.de FB 3: Mathematik Phone: +49 421 2182276 University of Bremen Secr.: +49 421 2184971 D-28334 Bremen Fax: +49 421 2184856 16-Jan-2002 19:05:00 -0400,1913;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 16 Jan 2002 19:05:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Qz0y-0003t1-00 for categories-list@mta.ca; Wed, 16 Jan 2002 18:58:40 -0400 From: Marcelo Fiore MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15429.60156.334106.44767@avon.cl.cam.ac.uk> Date: Wed, 16 Jan 2002 21:05:00 +0000 (GMT) To: categories@mta.ca Subject: categories: Preprint: Semantic Analysis of Normalisation by Evaluation. X-Mailer: VM 6.75 under 21.1 (patch 13) "Crater Lake" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk The preprint Semantic Analysis of Normalisation by Evaluation for Typed Lambda Calculus is available from http://www.cl.cam.ac.uk/~mpf23/papers/Types/nbe.ps.gz . The abstract follows. The paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and shows how it can be adapted to unify definability and normalisation, yielding an extensional normalisation result. In the second part of the paper the analysis is refined further by considering intensional Kripke relations (in the form of glueing) and shown to provide a function for normalising terms, casting normalisation by evaluation in the context of categorical glueing. The technical development includes an algebraic treatment of the syntax and semantics of the typed lambda calculus that allows the definition of the normalisation function to be given within a simply typed meta-theory. Best, Marcelo. 17-Jan-2002 09:04:02 -0400,1550;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 17 Jan 2002 09:04:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RCBk-0001dN-00 for categories-list@mta.ca; Thu, 17 Jan 2002 09:02:40 -0400 Message-Id: <200201171123.g0HBNjq29344@ithaca.mcs.le.ac.uk> To: categories@mta.ca Subject: categories: Final Coalgebra Question Mime-Version: 1.0 (generated by tm-edit 1.8) Content-Type: text/plain; charset=US-ASCII Date: Thu, 17 Jan 2002 11:23:46 +0000 From: N Ghani Sender: cat-dist@mta.ca Precedence: bulk Can anyone help me with the following final coalgebra questions 1. Let X be a fixed Set. What is the final coalgebra of the functor [X,_]:Set -> Set. If you wish to make X finite then that's fine by me. 2. Consider the functor [[_,2],2]:Set -> Set. This functor doesnt have a final coalgebra for cardinality reasons. However one may define a finitary variant of this functor as follows: First let TX = [[X,2],2] if X is finitely presentable. Thus T:Set_fp -> Set is a functor from the full subcategory of fintely presentable objects of Set into Set. Next define T' to be the left Kan extension of T along the inclusion Set_fp -> Set. In other words T'X is the filtered colimit of all the TX_0 where X_0 is a finitely presentable subobject of X Now, T' is clearly finitary and from general nonsense we know that it has a final coalgebra. But what is it concretely? Thanks for any help you can offer Neil 17-Jan-2002 09:04:05 -0400,2670;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 17 Jan 2002 09:04:05 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RCAY-0001db-00 for categories-list@mta.ca; Thu, 17 Jan 2002 09:01:26 -0400 Message-ID: <3C46A2F2.638AF892@bangor.ac.uk> Date: Thu, 17 Jan 2002 10:09:55 +0000 From: "Prof. T.Porter" X-Mailer: Mozilla 4.7 [en] (X11; I; FreeBSD 3.3-RELEASE i386) X-Accept-Language: en, fr MIME-Version: 1.0 To: "categories@mta.ca" Subject: categories: Kripke equivalence frames as coalgebras? Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Dear All, I note the large amount of activity in the study of coalgebras and am looking for a way to introduce elements of this into seminar discussions with a group of people working in parts of computer science and artificial intelligence that normally do not see much categorical light (and who have little categorical background). In a series of seminars I have been discussing epistemic logic (that is various extensions of the modal logic S5 and its multimodal versions) and have thus introduced Kripke equivalence frames as sets of possible worlds with an equivalence relation and have talked about their morphisms (bounded or p-morphisms to the modal logicians). Various coalgebraic sources make reference to Kripke frames as coalgebras for the power set functor, P : Sets -> Sets, but I have so far been unable to find a relatively elementary treatment of cofree coalgebras for this context. The `dual' category (for the S5 case) is of monadic algebras and it has free algebras but I have been trying to avoid using duality too much in the seminars I have been giving and certainly do not want to go into questions of `generalised frames'. Explicitly I would like references for answers to the following: (i) Is there a clear description in the literature (e.g. in coequational form or categorically) of the category of Kripke \emph{equivalence} frames as coalgebras? (ii) Where can I find descriptions (as direct and simple as possible!) of limits in the category of equivalence frames (or does the lack of a complete duality muck things up as it does in the category of ALL Kripke frames) (iii) Given a Kripke equivalence frame, F, is there a nice cofree coalgebra construction which is not `too horrendous for words' e.g. avoiding going via canonical models and the like. Thanking you all in advance, and slightly belated Happy New Year to everyone, Tim Porter 17-Jan-2002 09:10:15 -0400,3268;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 17 Jan 2002 09:10:15 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RCIm-0001xA-00 for categories-list@mta.ca; Thu, 17 Jan 2002 09:09:56 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 17 Jan 2002 08:03:09 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: categorical incunabula In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk I have never checked this out, but Fred Linton mentioned on more than one occasion that Harald Bohr constructed his eponymous compactification of abelian groups using a construction which was essentially the same as the proof of the GAFT. Take the product of "all" the compact groups generated by a given group and then the closure of the subgroup there. Actually, I have always felt that the GAFT really doesn't tell you much that isn't evident. The SAFT, on the other hand, really does do something non-trivial. On Mon, 14 Jan 2002, Hans-E. Porst wrote: > Concerning Peter Freyd's question > > > Saunders's 1948 paper (without Sammy) first surprised me 40 years ago. > > Buchsbaum in his 1955 paper that introduced abelian categories (under > > the name "exact categories") said that he saw no way of defining > > infinite products. Which meant that he hadn't seen Saunders's 1948 > > paper. Is this the first appearance of universal mapping definitions? > > one certainly might consider A.A. Markov's definition of a free topological > group (in 1945) as an earlier appearance: > > A. A. Markov: On free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 9 > (1945), 3-64 [Amer. Math. Soc. Transl. 30 (1950), 11-88; Reprint: Amer. > Math. Soc. Transl. Ser. I, 8 (1962), 195-272.] > > Note, in this context, also the early apperances of what we now would call > "applications (or predecessors) of Freyd's GAFT" (though none of these > papers has the notions of category or functor) > > S. Kakutani: Free topological groups and finite discrete product groups, > Proc. Imp. Acad. Tokyo 20 (1944), 595-598 > > P. Samuel: On universal mappings and free topological groups, Bull. Amer. > Math. Soc. 54 (1948), 591-598 > > In his 1957 paper > > A. I. Malcev: Free topological algebras, Izv. Akad. Nauk SSSR Ser. Mat. 21 > (1957), 171-198 [Amer. Math. Soc. Transl. Ser. II, 17 (1961), 173-200.] > > Malcev already begins his proof of the existence of a free topological > algebra (as a topological subgroup of the corresponding product) with the > phrase "In the usual way one can now prove". > > -- > Hans-E. Porst porst@math.uni-bremen.de > FB 3: Mathematik Phone: +49 421 2182276 > University of Bremen Secr.: +49 421 2184971 > D-28334 Bremen Fax: +49 421 2184856 > > > > > 18-Jan-2002 08:31:43 -0400,2949;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:31:43 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RY3l-0007ks-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:23:53 -0400 Message-ID: <3C46E55A.B1928DC4@email.unc.edu> Date: Thu, 17 Jan 2002 09:53:14 -0500 From: jim stasheff X-Mailer: Mozilla 4.79 [en] (WinNT; U) X-Accept-Language: en MIME-Version: 1.0 To: "categories@mta.ca" Subject: categories: Re: Kripke equivalence frames as coalgebras? References: <3C46A2F2.638AF892@bangor.ac.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk "Prof. T.Porter" wrote: > > Dear All, > > I note the large amount of activity in the study of coalgebras and am > looking for a way to introduce elements of this into seminar discussions > with a group of people working in parts of computer science and > artificial intelligence that normally do not see much categorical light > (and who have little categorical background). In a series of seminars I > have been discussing epistemic logic (that is various extensions of the > modal logic S5 and its multimodal versions) and have thus introduced > Kripke equivalence frames as sets of possible worlds with an equivalence > relation and have talked about their morphisms (bounded or p-morphisms > to the modal logicians). > > Various coalgebraic sources make reference to Kripke frames as > coalgebras for the power set functor, P : Sets -> Sets, but I have so > far been unable to find a relatively elementary treatment of cofree > coalgebras for this context. The `dual' category (for the S5 case) is > of monadic algebras and it has free algebras but I have been trying to > avoid using duality too much in the seminars I have been giving and > certainly do not want to go into questions of `generalised frames'. > Explicitly I would like references for answers to the following: > (i) Is there a clear description in the literature (e.g. in coequational > form or categorically) of the category of Kripke \emph{equivalence} > frames as coalgebras? > (ii) Where can I find descriptions (as direct and simple as possible!) > of limits in the category of equivalence frames (or does the lack of a > complete duality muck things up as it does in the category of ALL Kripke > frames) > (iii) Given a Kripke equivalence frame, F, is there a nice cofree > coalgebra construction which is not `too horrendous for words' e.g. > avoiding going via canonical models and the like. > > Thanking you all in advance, > and slightly belated Happy New Year to everyone, > > Tim Porter I think both Michaelis and Block have written on cofree coalgebras and Michaelis is nearing completion of a lengthy survey article on coalgebras. jim 18-Jan-2002 08:31:45 -0400,2810;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:31:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RY8k-0008LH-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:29:02 -0400 From: To: "'categories@mta.ca'" Message-ID: <4ACB46914615D311BA320008C79F3E2E018F2C03@ffmexch1.ffm.sdm.de> Subject: categories: Re: Final Coalgebra Question Date: Thu, 17 Jan 2002 22:13:45 +0100 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2653.19) Content-Type: text/plain; charset="windows-1252" Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Hi, 1. That's pretty easy. Since [X,_] maps the one-element (final) set onto itself, i.e., it preserves the final object, the final coalgebra of this functor is nothing but the one-element-set itself. Of course one need not use this abstract argument ("the forgetful functor U:Set_F --> Set creates any limit which the functor F:Set->Set preserves") but can give a direct proof. 2. That's much more complicated. I do not know any elementary description. For one possible description as a quotient of an automaton you may refer to H. Peter Gumm, Tobias Schroeder : Coalgebras of bounded type. Mathematical Structures in Computer Science, to appear which you can find Peter Gumm's homepage (http://www.mathematik.uni-marburg.de/~gumm/Papers/publ.html) and the papers quoted there. ... If somebody could offer a really nice description of that final coalgebra this would be quite interesting I assume. Hope that helps a bit Tobias Schroeder -----Original Message----- From: N Ghani To: categories@mta.ca Cc: coalgebras@iti.cs.tu-bs.de Sent: 17.01.02 12:23 Subject: coalgebras: Final Coalgebra Question Can anyone help me with the following final coalgebra questions 1. Let X be a fixed Set. What is the final coalgebra of the functor [X,_]:Set -> Set. If you wish to make X finite then that's fine by me. 2. Consider the functor [[_,2],2]:Set -> Set. This functor doesnt have a final coalgebra for cardinality reasons. However one may define a finitary variant of this functor as follows: First let TX =3D [[X,2],2] if X is finitely presentable. Thus T:Set_fp -> Set is a functor from the full subcategory of fintely presentable objects of Set into Set. Next define T' to be the left Kan extension of T along the inclusion Set_fp -> Set. In other words T'X is the filtered colimit of all the TX_0 where X_0 is a finitely presentable subobject of X Now, T' is clearly finitary and from general nonsense we know that it has a final coalgebra. But what is it concretely? Thanks for any help you can offer Neil 18-Jan-2002 08:31:46 -0400,3073;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:31:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RY4h-00079p-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:24:51 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 17 Jan 2002 10:10:10 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Final Coalgebra Question In-Reply-To: <200201171123.g0HBNjq29344@ithaca.mcs.le.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk On Thu, 17 Jan 2002, N Ghani wrote: > > Can anyone help me with the following final coalgebra questions > > 1. Let X be a fixed Set. What is the final coalgebra of the functor > [X,_]:Set -> Set. If you wish to make X finite then that's fine by me. For any functor T on any category with an initial object 0, T0 = 0 implies that 0 is the initial T-algebra. In this case, [X,1] = 1 implies that 1 is the final coalgebra. Not very interesting. > > 2. Consider the functor [[_,2],2]:Set -> Set. This functor doesnt have > a final coalgebra for cardinality reasons. However one may define a > finitary variant of this functor as follows: > > First let TX = [[X,2],2] if X is finitely presentable. Thus T:Set_fp > -> Set is a functor from the full subcategory of fintely presentable > objects of Set into Set. Next define T' to be the left Kan extension > of T along the inclusion Set_fp -> Set. In other words T'X is the > filtered colimit of all the TX_0 where X_0 is a finitely presentable > subobject of X > > Now, T' is clearly finitary and from general nonsense we know that it > has a final coalgebra. But what is it concretely? > Unless I am missing something, a finitely presented (or finitely generated) set is just finite. Now the functor 2^{2^-} is the free complete atomic boolean algebra triple (or rather the functor part thereof). The best way to see this is that 2^- is adjoint to itself on the right and tripleable so that the category of algebras is Set^op. The same argument for finite sets gives free boolean algebras and the colimit extension to all sets gives the same since the theory is finitary. The functor T' produces finite sets of finite subsets. Although not related to Neil's question, it is interesting to point out that the duality between finite sets and finite boolean algebras extends to a duality between the limit completion of one and the colimit completion of the other. Applied in one way this gives Stone duality between boolean algebras and profinite sets (i.e. Stone spaces) and the other way gives the duality between sets and profinite boolean algebras, which is complete atomic boolean algebras. > Thanks for any help you can offer > > Neil > > > 18-Jan-2002 08:31:49 -0400,1382;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:31:49 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RY68-00087M-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:26:20 -0400 Date: Thu, 17 Jan 2002 10:32:40 -0800 Message-Id: <200201171832.KAA07744@kamiak.eecs.wsu.edu> From: "David Benson" To: categories@mta.ca Subject: categories: rfn+rfr Sender: cat-dist@mta.ca Precedence: bulk Dear Colleagues, We are in the presence of a functor F: A --> B which is surjective on the objects of B, up to isomorphism. I suppose I could call such functors ``soouti'', but I am hoping that someone will suggest a better name. Somewhat related, I have not been able to discover the definition of ``essential image'' in print, and I would greatly appreciate a reference, preferably the first one. Thank you very much in advance! Cheers, David -- Professor David B. Benson (509) 335-2706 School of EE and Computer Science (EME 102) (509) 335-3818 fax PO Box 642752, Washington State University office: Sloan 308 and 307 Pullman WA 99164-2752 U.S.A. dbenson@eecs.wsu.edu ---------------------------------------------------------------------------------- 18-Jan-2002 08:31:52 -0400,1180;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:31:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RY53-0007zF-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:25:13 -0400 Date: Thu, 17 Jan 2002 10:28:41 -0500 (EST) From: Oswald Wyler To: Subject: categories: Bourbaki's GAFT Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Bourbaki decided not to use categories in Elements de Mathematique (accents omitted because they can be disfigured in transit), but his Chapitre IV, Structures, of Theorie des Ensembles, published in 1957, has a decidedly categorical flavor. He defines applications universelles (universal maps) in full generality, and in Section 3.2, he gives a criterion for the existence of universal maps which, rewritten in categorical terms, becomes Freyd's GAFT, with the usual proof. Question: add Bourbaki's chapter to the Incunabula? Oswald Wyler 18-Jan-2002 08:32:20 -0400,2104;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:32:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RY9n-000724-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:30:07 -0400 Message-ID: <3C47B1F9.F32ABFFB@kestrel.edu> Date: Thu, 17 Jan 2002 21:26:18 -0800 From: Dusko Pavlovic X-Mailer: Mozilla 4.73 [en] (X11; I; Linux 2.2.18-4hpmac ppc) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: Final Coalgebra Question References: <200201171123.g0HBNjq29344@ithaca.mcs.le.ac.uk> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk > 1. Let X be a fixed Set. What is the final coalgebra of the functor > [X,_]:Set -> Set. If you wish to make X finite then that's fine by me. you mean exponentiation? why isn't 1 --->[X,1] final? > 2. Consider the functor [[_,2],2]:Set -> Set. This functor doesnt have > a final coalgebra for cardinality reasons. However one may define a [snip] > Now, T' is clearly finitary and from general nonsense we know that it > has a final coalgebra. But what is it concretely? depends on how we represent the final coalgebra for the finite powerset functor [-,2]_fin. if you like to view its elements as finitely branching apgs, then the final coalgebra for [[-,2],2]_fin presumably consists of *bipartite* finitely branching apgs: the root is blue, its successors are red, the successors of successors are blue again, and so on. (given a coalgebra X-->[[X,2],2], write Y = [X,2]. this is the set of the red nodes of this apg; X is the set of the blue nodes. each of the red nodes the char function of its blue successors. and the structure map X-->[Y,2] tells the red successors of each blue node. so each elt of X induces, as its trace through the coalgebra, a bipartite apg with a blue root. this gives the final coalgebra homomorphism from X to the blue-rooted bipartite apgs. unless i am wrong.) -- dusko 18-Jan-2002 08:34:03 -0400,897;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 08:34:03 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RYAn-00085q-00 for categories-list@mta.ca; Fri, 18 Jan 2002 08:31:09 -0400 Message-ID: <3C47BE20.A32EE197@maths.usyd.edu.au> Date: Fri, 18 Jan 2002 17:18:08 +1100 From: Steve Lack Organization: School of Mathematics and Statistics, University of Sydney X-Mailer: Mozilla 4.77 [en] (X11; U; OSF1 V5.1 alpha) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Reference needed Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Does anyone know of a reference for the fact that retracts of free categories (on a graph, that is) are free? Steve Lack. 18-Jan-2002 18:54:06 -0400,3139;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 18:54:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RhsF-0004w6-00 for categories-list@mta.ca; Fri, 18 Jan 2002 18:52:39 -0400 Message-ID: <3C488291.E2FD5522@cwi.nl> Date: Fri, 18 Jan 2002 21:16:17 +0100 From: Alexander Kurz Organization: CWI X-Mailer: Mozilla 4.75 [en] (X11; U; SunOS 5.6 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CfP: Categorical Methods for Concurrency, Interaction, and Mobility Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk [ Apologies for multiple copies ] Workshop on CATEGORICAL METHODS FOR CONCURRENCY, INTERACTION, AND MOBILITY Brno, Czech Republic, 24 August 2002 affiliated with CONCUR 2002 First Announcement and Call for Papers Aims and Scope: The aim of the workshop is to bring together researchers applying category theory to concurrency, interaction, or mobility. Topics of interest include, but are not limited to: categorical algebras of processes categorical methods in game semantics and geometry of interaction categorical models of term/graph rewriting or rewriting logic Chu spaces coalgebras, bialgebras, coinduction comparing models of concurrency enriched categories of processes interaction categories presheaf models Programme Committee: Samson Abramsky (Oxford) Thomas Hildebrandt (Copenhagen) Alexander Kurz (Amsterdam) Ugo Montanari (Pisa) Prakash Panangaden (Montreal) Horst Reichel (Dresden) Jiri Rosicky (Brno) Bob Walters (Como) Important dates: Deadline for submission: May 24, 2002 Notification of acceptance: July 5, 2002 Final version due: July 25, 2002 Workshop: August 24, 2002 Location: The workshop will be held in Brno in August 2002. It is a satellite workshop of CONCUR 2002. For venue and registration see the CONCUR web page at http://www.fi.muni.cz/concur2002/ Submissions: It is planned to publish the proceedings of the meeting as a volume in Elsevier's ENTCS series. Papers must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Papers should be submitted as PostScript files by email to kurz@cwi.nl, containing `CMCIM-submission' in the subject. A separate message should also be sent (subject: CMCIM-abstract), containing authors, title, a text-only abstract, as well as mailing addresses (both postal and electronic) of the corresponding author. Workshop organizer: Alexander Kurz CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands email: kurz@cwi.nl Further information at http://www.cwi.nl/cmcim or from kurz@cwi.nl -- http://www.cwi.nl/~kurz 18-Jan-2002 18:54:09 -0400,1615;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 18:54:09 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RhpN-0005zH-00 for categories-list@mta.ca; Fri, 18 Jan 2002 18:49:41 -0400 Date: Fri, 18 Jan 2002 18:22:12 +0100 From: Frank Atanassow To: categories@mta.ca Subject: categories: Re: rfn+rfr Message-ID: <20020118182212.A15391@cs.uu.nl> References: <200201171832.KAA07744@kamiak.eecs.wsu.edu> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i In-Reply-To: <200201171832.KAA07744@kamiak.eecs.wsu.edu>; from dbenson@eecs.wsu.edu on Thu, Jan 17, 2002 at 10:32:40AM -0800 Sender: cat-dist@mta.ca Precedence: bulk David Benson wrote (on 17-01-02 10:32 -0800): > We are in the presence of a functor F: A --> B which is > surjective on the objects of B, up to isomorphism. > I suppose I could call such functors ``soouti'', > but I am hoping that someone will suggest a better name. "Essentially surjective", unless I am missing something. > Somewhat related, I have not been able to discover the > definition of ``essential image'' in print, > and I would greatly appreciate a reference, preferably the first one. Taylor's "Practical Foundations" mentions "representative image" on p.210, which I take it is the same thing. -- Frank Atanassow, Information & Computing Sciences, Utrecht University Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands Tel +31 (030) 253-3261 Fax +31 (030) 251-379 18-Jan-2002 18:54:44 -0400,2857;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 18 Jan 2002 18:54:44 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Rhu9-0005pA-00 for categories-list@mta.ca; Fri, 18 Jan 2002 18:54:37 -0400 Date: Fri, 18 Jan 2002 12:12:37 +0000 From: David Clark To: categories@mta.ca Subject: categories: jobs: Five Lectureships at King's College London Message-ID: <20020118121236.C16175@calcium.dcs.kcl.ac.uk> Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Disposition: inline User-Agent: Mutt/1.2.5i Content-Transfer-Encoding: quoted-printable X-MIME-Autoconverted: from 8bit to quoted-printable by calcium.dcs.kcl.ac.uk id MAA16275 Sender: cat-dist@mta.ca Precedence: bulk Five Lectureships at King's College London Department Of Computer Science=20 School Of Physical Science And Engineering=20 As part of a major new initiative, the Department of Computer Science is seeking to fill FIVE new lectureships. Candidates who are able to show a strong research orientation and a commitment to teaching are invited to apply for these positions. The Department currently has four strong research groups:=20 Algorithm Design: design, analysis and engineering of algorithms in a variety of combinatorical settings including bioinformatics, musicology and operations research. Software Engineering: including analysis of programming languages, object-orientated notations and tools, semantics, specifications, logic, artificial intelligence.Applications within legal-reasoning, business processing, e-commerce. Logic and Computation: logics, artificial intelligence, reasoning and deduction, proof systems. Natural Language Processing: logical foundations of computational semantics, computational syntax and grammar development, dialogue interpretations and management systems. The appointments will be made on an appropriate point of either the Lecturer A scale (currently =A3 19,585 to =A3 26,327 per annum) or Lecturer B scale (currently =A3 27,337 to =A3 34,349 per annum), which includes =A3 2,134 London Allowance. For an applicaton form and further details, please contact Ebony Kenton, Personnel Department, King?s College London, Strand, London WC2R 2LS or email ebony.kenton@kcl.ac.uk quoting reference A1/CCS/86/01. The closing date for receipt of applications is 31 January 2002.=20 For further information please contact Professor Tom Maibaum by email only at tom@dcs.kcl.ac.uk Equality of opportunity is College policy=20 --=20 _______________________________________________________ David Clark, room 9DA, Department of Computer Science,=20 King's College London, The Strand, London, WC2R 2LS, UK.=20 ph: +44 20 7848 2472 19-Jan-2002 09:31:38 -0400,902;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 19 Jan 2002 09:31:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16RvSU-0000oK-00 for categories-list@mta.ca; Sat, 19 Jan 2002 09:22:58 -0400 Date: Sat, 19 Jan 2002 08:20:16 -0500 (EST) From: Peter Freyd Message-Id: <200201191320.g0JDKGp18945@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: representative image Sender: cat-dist@mta.ca Precedence: bulk David Benson wrote (on 17-01-02 10:32 -0800): > We are in the presence of a functor F: A --> B which is > surjective on the objects of B, up to isomorphism. > I suppose I could call such functors ``soouti'', > but I am hoping that someone will suggest a better name. In Cats and Allegators we say (1.31, p17) that the functor has a REPRESENTATIVE IMAGE. 22-Jan-2002 10:34:24 -0400,4293;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 22 Jan 2002 10:34:24 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16T1s2-0006wN-00 for categories-list@mta.ca; Tue, 22 Jan 2002 10:25:54 -0400 From: Peter Selinger Message-Id: <200201212015.g0LKFNw31911@quasar.mathstat.uottawa.ca> Subject: categories: CFP: CTCS'02 and Grad Student Preconference To: categories@mta.ca (Categories List) Date: Mon, 21 Jan 2002 15:15:23 -0500 (EST) X-Mailer: ELM [version 2.5 PL3] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk CATEGORY THEORY AND COMPUTER SCIENCE (CTCS'02) AUGUST 15-17, 2002 GRADUATE STUDENT PRECONFERENCE AUGUST 12-14, 2002 University of Ottawa Ottawa, Ontario, Canada SECOND CALL FOR PAPERS CTCS '02 is the 9th Conference on Category Theory and Computer Science. The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory. The emphasis is upon applications of category theory, but it is recognized that the area is highly interdisciplinary. Typical topics of interest include, but are not limited to, category-theoretic aspects of the following: coalgebras and computing concurrent and distributed systems constructive mathematics declarative programming and term rewriting domain theory and topology foundations of computer security linear logic modal and temporal logics models of computation program logics, data refinement, and specification programming language semantics type theory Previous meetings have been held in Guildford (Surrey), Edinburgh (twice), Manchester, Paris, Amsterdam, Cambridge, and S. Margherita Ligure (Genova). This is the first time CTCS will be held in North America. The proceedings of the conference will be published as a special issue of ENTCS (Electronic Notes in Theoretical Computer Science). Paper copies of the proceedings will be available to participants at the conference. GRADUATE STUDENT PRECONFERENCE One new feature that CTCS will have this year is a "preconference" from August 12-14. The goal is to prepare students for CTCS, through mini-courses in the basic areas underlying the fields of the conference. We anticipate offering courses in the following areas: Introduction to Category Theory Introduction to Categorical Logic Communication and Concurrency Game Semantics Linear Logic Please contact us if you have graduate students or advanced undergraduates who you think would be interested in attending. The preconference will be partially funded by Centre de Recherches Mathematiques (CRM, Montreal). A limited number of student travel grants will be available; please contact the local organizers for details. PROGRAMME COMMITTEE Rick Blute, Chair (Ottawa) Robin Cockett (Calgary) Thierry Coquand (Chalmers) Andrea Corradini (Pisa) Thomas Ehrhard (Luminy) Ryu Hasegawa (Tokyo) Martin Hofmann (Munich) Bart Jacobs (Nijmegen) Michael Johnson (Macquarie) Dusko Pavlovic (Kestrel Institute) Alex Simpson (Edinburgh) ORGANIZING COMMITTEE E. Moggi, Chair, (Genova) S. Abramsky (Oxford) P. Dybjer (Chalmers) B. Jay (Sydney) A. Pitts (Cambridge) LOCAL ORGANIZING COMMITTEE R. Blute (Ottawa) P. Scott (Ottawa) SUBMISSION OF PAPERS Papers should be submitted, preferably in electronic form, to ctcs02@mathstat.uottawa.ca. Papers are limited to 15 pages, and must be submitted in dvi, postscript, or pdf format, possibly gzipped and/or uuencoded, or sent as a standard email attachment. All submissions must be received by March 25th, 2002. If you cannot submit your paper electronically, please contact the program chair at ctcs02@mathstat.uottawa.ca. IMPORTANT DATES March 25th, 2002 Submission deadline May 20th, 2002 Notification of authors of accepted papers CONFERENCE HOMEPAGE Updated information is available from http://www.mathstat.uottawa.ca/lfc/ctcs2002/. 22-Jan-2002 10:34:27 -0400,1158;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 22 Jan 2002 10:34:27 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16T1pt-0006lq-00 for categories-list@mta.ca; Tue, 22 Jan 2002 10:23:41 -0400 Date: Mon, 21 Jan 2002 12:58:35 +0000 (GMT) From: Robert Byrne To: categories@mta.ca Subject: categories: Kan extensions In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Dear Category Theory list, I would like to know if anyone has any references regarding the use of the computation of Kan extensions as a model of computation (e.g. how powerful is some given algorithm as compared to a Turing machine). I have seen the Walters-Carmody algorithm in 'Categories and Computer Science', but there is no mention there of the computational power of the algorithm presented. Any information would be welcome. Yours, -- Robert Byrne 23-Jan-2002 08:39:46 -0400,4207;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 23 Jan 2002 08:39:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16TMdG-0007fW-00 for categories-list@mta.ca; Wed, 23 Jan 2002 08:36:02 -0400 From: Chin Wei Ngan Message-Id: <200201230250.KAA29632@sf0.comp.nus.edu.sg> Subject: categories: CFP : ACM SIGPLAN ASIA-PEPM 2002 To: categories@mta.ca Date: Wed, 23 Jan 2002 10:50:07 +0800 (GMT-8) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk CALL FOR PAPERS : ASIA-PEPM 2002 ACM SIGPLAN ASIAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation Aizu, JAPAN, September 12-14 2002 http://www.comp.nus.edu.sg/asia-pepm02 (co-located with 6th Intl. Symp. on Functional and Logic Programming) Submission deadline: 1st March 2002 The ASIA-PEPM'02 symposium will bring together researchers working in the areas of semantics-based program manipulation, partial evaluation, and program analysis. The symposium focuses on techniques, supporting theory, and applications for the analysis and manipulation of programs. Technical topics include, but are not limited to: * Program manipulation techniques: transformation, specialization, normalization, reflection, rewriting, run-time code generation, multi-level programming. * Program analysis techniques: abstract interpretation, static analysis, binding-time analysis, type-based analysis. * Related issues in language design and models of computation: imperative, functional, logical, constraint-based, object-oriented, parallel, concurrent, secure, domain-specific. * Programs as data objects: staging, meta-programming, incremental computation, mobility, tools and techniques, prototyping and debugging. * Applications: systems programming, scientific computing, embedded systems, graphics, security, model checking, compiler generation, compiler optimization, decompilation. Original results that bear on these and related topics are solicited. Papers investigating novel uses and applications of program manipulation are especially encouraged. Authors concerned about the appropriateness of a topic are welcome to consult with the program chair prior to submission. SUBMISSION INFORMATION Papers should be submitted electronically via the workshop's Web page. Exceptionally, submissions may be emailed to the program chair: asiapepm@comp.nus.edu.sg. Acceptable formats are PostScript or PDF, viewable by gv. Submissions should not exceed 5000 words, excluding bibliography and figures. Submitted papers will be judged on the basis of significance, relevance, correctness, originality, and clarity. They should clearly identify what has been accomplished and why it is significant. The work described should not have been previously published in a major forum. Authors must indicate if a closely related paper is also being considered for another conference or journal. The proceeding of the symposium will be published by ACM Press. A special issue of Higher-Order Symbolic Computation is also planned. LOCAL ARRANGEMENT Mizuhito Ogawa (JST, Japan) GENERAL CHAIR Kenichi Asai (Ochanomizu University, Japan) PROGRAM CHAIR Wei-Ngan Chin (National University of Singapore, Singapore) PROGRAM COMMITTEE Manuel Chakravarty (University of New South Wales, Australia) Tyng-Ruey Chuang (Academia Sinica, Taiwan) Charles Consel (ENSEIRB, France) Oege de Moor (University of Oxford, UK) Masami Hagiya (University of Tokyo, Japan) Nevin Heintze (Agere Systems, USA) Neil Jones (Univ of Copenhagen, Denmark) Yanhong Annie Liu (SUNY at Stony Brook, USA) Atsushi Ohori (JAIST, Japan) Alberto Pettorossi (University of Roma, Italy) Simon Peyton Jones (Microsoft, UK) Carolyn Talcott (SRI International, USA) Zhe Yang (University of Pennsylvania, USA) 23-Jan-2002 08:44:28 -0400,2242;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 23 Jan 2002 08:44:28 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16TMlE-0007M7-00 for categories-list@mta.ca; Wed, 23 Jan 2002 08:44:16 -0400 Message-ID: <000401c1a3f5$58326fe0$2e438cd4@brown1> From: "Ronald Brown" To: References: Subject: categories: Re: Kan extensions Date: Tue, 22 Jan 2002 16:57:08 -0000 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Sender: cat-dist@mta.ca Precedence: bulk reply to r.brown@bangor.ac.uk Robert There is a paper R. Brown and Anne Heyworth, `Using rewriting systems to compute left Kan extensions and induced actions of categories', J. Symbolic Computation 29 (2000) 5-31. which does not answer your question on power but instead shows that the Knuth-Bendix process for computing complete rewrite systems for presentations of monoids can be extended to `presentations of Kan extensions'. The method seems different from that of Carmody-Walters, but was inspired by it. See Anne's home page at Leicester for more papers in this area. The `power' of the K-B method is improved since it applies to more examples. Ronnie Brown ----- Original Message ----- From: "Robert Byrne" To: Sent: Monday, January 21, 2002 12:58 PM Subject: categories: Kan extensions > Dear Category Theory list, > > I would like to know if anyone has any references regarding the use of the > computation of Kan extensions as a model of computation (e.g. how powerful > is some given algorithm as compared to a Turing machine). I have seen the > Walters-Carmody algorithm in 'Categories and Computer Science', but there > is no mention there of the computational power of the algorithm presented. > > Any information would be welcome. > > Yours, > > -- > Robert Byrne > > > > > 23-Jan-2002 08:45:04 -0400,5395;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 23 Jan 2002 08:45:04 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16TMlw-0008G1-00 for categories-list@mta.ca; Wed, 23 Jan 2002 08:45:00 -0400 To: categories@mta.ca Subject: categories: preprints: Abstract Stone Duality papers Message-Id: From: Paul Taylor Date: Wed, 23 Jan 2002 12:08:43 +0000 X-Ident: pt Sender: cat-dist@mta.ca Precedence: bulk This is to invite your comments on Sober Spaces and Continuations Subspaces in Abstract Stone Duality Paul Taylor http://www.dcs.qmul.ac.uk/~pt/ASD/ These two papers are, at last, complete and have been submitted to a journal. You can get them in various formats from this web address. Together they develop the idea (that I first promoted in 1993) of a category whose dual is monadic over the category itself. This was inspired by Bob Pare's 1973 result for an elementary topos that the contravariant powerset functor, which is self-adjoint, is monadic. The category of locally compact sober spaces has the same property, with the topology in place of the powerset. Topological ideas, including compact Hausdorff and overt discrete spaces, were developed in the paper Geometric and Higher Order Logic in terms of ASD that appeared in TAC in December 2000. That paper relied mainly on lattice-theoretic ideas, but "Sober Spaces..." is an introduction to the impact of the monadic property on computation and topology. (The Web page also has a non-technical "manifesto".) "Sober Spaces..." actually discusses the weaker situation where the dual category is a full subcategory of the category of algebras. This happens exactly when every object is the equaliser of a certain diagram that arises from the monad. We call this property "sobriety", although it is defined in terms of a (restricted) lambda-calculus instead of lattice theory; the paper explains the connection between the two. The categorical construction that turns any category with an exponentiating object Sigma into one in which all objects are sober is essentially the same as that used by Thielecke, Fuhrmann and Selinger to study continuations. (However, ours makes little use of Power and Robinson's notion of "premonoidal category".) A corresponding "sober" lambda calculus is given. Our new "focus" operator is similar to the operator "force" that Thielecke et al. discuss, except that its use is restricted to the situation where there is NO computational effect, so it is denotational and does not depend on an order of evaluation. All powers of Sigma are automatically sober, so the only type in the restricted lambda calculus that needs to be considered is N. The sober calculus is shown to be equivalent to adding a "description" operator (a la Russell) to the restricted lambda calculus with primitive recursion and the lattice operations. The corollary of this is that any map $\Sigma^N\to\Sigma^U$ is a homomorphism with respect to the monad iff it preserves finite meets and the existential quantifier over N. This is the base case in showing that locale theory is captured by our lambda calculus. The extension from N to arbitrary types depends on the fixed point axiom, which is discussed (for the first time within ASD) in the paper on domain theory that I have just started writing. The introductory role of "Sober Spaces..." is concluded with a brief explanation of how and why the calculus may be compiled into pure PROLOG. "Subspaces in ASD" completes the journey to the monadic situation. It begins by explaining how the monadic property abstracts the 1930s results of Stone, Tarski and Lindenbaum, and then how Beck's theorem relates it to the subspace topology and injectivity of Sigma. We say that $i:X\to Y$ is a "Sigma-split subspace" if "open subsets" of X (maps $X\to\Sigma$) are expanded to open subsets of Y by means of a morphism $I:\Sigma^X\to\Sigma^Y$. As is remarked in the conclusion, this is really too strong. The paper gives three constructions of the monadic completion of a category. The first formally adjoins Sigma-split equalisers in a way similar to the Karoubi construction for splitting idempotents. The second is the opposite of the category of algebras, the crucial point being the construction of coproducts of algebras; this is the result that I had in 1993. The third construction is a further extension of the sober lambda calculus, now adding "subtypes" with a comprehension-like constructor. The extra operator on terms, called "admit", plays a similar role to "focus" in the sober calculus. I presented preliminary results about this calculus at the APPSEM meeting in Darmstadt in March 2001. The comprehension calculus has a normalisation theorem, the computational import of which is that "i" and "admit" serve only as compile-time type-annotations on terms, and may be erased for execution. The paper concludes with applications to coproducts (which clearly exhibits the continuation-passing style) and to the quotient of an overt discrete object by an open equivalence relation (which was constructed in "Geometric and Higher Order Logic"). Paul Taylor (no academic affiliation) 23-Jan-2002 15:09:12 -0400,1835;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 23 Jan 2002 15:09:12 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16TSfN-0001hL-00 for categories-list@mta.ca; Wed, 23 Jan 2002 15:02:41 -0400 User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.02.2106 Date: Wed, 23 Jan 2002 19:59:24 +0000 Subject: categories: (lluf)+(2==>3)=? From: jean benabou To: Category List Message-ID: Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk There have been many mails about lluf subcategories X' of a category X. In many meaningful cases such subcategories satisfy the following extra property: (2==>3) If two maps of a commutative triangle of X belong to X' so does the third. Examples of such X's are : the maps f of X which are inverted by a functor F:X-->Y, or those such that F(f) is an identity, i.e. the "vertical" maps. If X is a groupoid a subcategry X' of X need not be a subgroupoid. It is iff it satisfies (2==> 3). I would like to know if the property (lluf)+(2==>3) , which has certainly been met by many people, has a name. (It certainly deserves to be named). In case it does not have one, I am tempted by: "X' is a strip of X", or even better: "X' is a wide strip of X" The second name would permit to use "strip" for (2==>3) and "wide", a la Ronnie Brown, for lluf. It is easy to translate, e.g. in French by "large bande", and to me it seems descriptive and flexible. But of course English is not my mother tongue, and I am open to all suggestions. Thanks, and, a bit late, a happy New Year to all.. 25-Jan-2002 15:14:23 -0400,1931;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 25 Jan 2002 15:14:23 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16UBgz-0005hA-00 for categories-list@mta.ca; Fri, 25 Jan 2002 15:07:17 -0400 Message-Id: <200201251849.g0PImu821852@math.u-strasbg.fr> Date: Fri, 25 Jan 2002 19:48:56 +0100 (MET) From: Philippe Gaucher Reply-To: Philippe Gaucher Subject: categories: preprint: Unifying The Globular and The Topological Approach of Dihomotopy To: Category List X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4.2 SunOS 5.8 sun4u sparc Content-Type: text X-Sun-Text-Type: ascii Sender: cat-dist@mta.ca Precedence: bulk Hello, The following preprint is available. Comments are welcome. Title : Unifying The Globular and The Topological Approach of Dihomotopy Abstract : We introduce the category of flows and an equivalence relation on it called weak dihomotopy. The category of globular CW-complexes introduced in math.AT/0107060 can be embedded in a canonical way into the category of flows. This embedding induces a category equivalence from the category of globular CW-complexes up to dihomotopy and the one of flows up to weak dihomotopy. This statement is proved thanks to a directed version of Whitehead's theorem (the one concerning the equivalence between weak homotopy and homotopy for CW-complex). So studying HDA up to dihomotopy is equivalent to working within the category of flows. This setting is better than the one of globular CW-complexes because the category of flows is complete and cocomplete. Url : http://www-irma.u-strasbg.fr/~gaucher/dspace.ps http://www-irma.u-strasbg.fr/~gaucher/dspace.pdf http://www-irma.u-strasbg.fr/~gaucher/dspace.ps.gz http://www-irma.u-strasbg.fr/~gaucher/dspace.pdf.gz 28-Jan-2002 11:12:01 -0400,3475;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 28 Jan 2002 11:12:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VDJG-0005eF-00 for categories-list@mta.ca; Mon, 28 Jan 2002 11:03:04 -0400 Message-Id: To: categories-list@mta.ca Date: Fri, 25 Jan 2002 13:17:44 GMT Message-Id: <200201251317.g0PDHiL12672@tosca.crn.cogs.susx.ac.uk> From: Vladimiro Sassone To: categories@mta.ca Subject: categories: CFP: F-WAN: Foundations of Wide Area Network Computing Sender: cat-dist@mta.ca Precedence: bulk =09 F-WAN: Foundations of Wide Area Network Computing =09=09 =09=09 co-located with ICALP2002 =09=09 12-13 July 2002, M=E1laga Spain =09=09Second announcement and Call for papers ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Aims and Scope The growing diffusion of internet services and applications is promoting global computing as an emerging model of computation. Based on mobility of code and computation on networks with highly dynamic topologies, the model needs effective infrastructures to support the coordination and control of components loaded at runtime from untrusted sources, as well as semantic frameworks to reason on the behaviour and properties of applications.=20 Foundations of Wide Area Network Computing focuses on semantics aspects of global computing, and invites submissions of original scientific work thereof. A non-exclusive list of topics includes: calculi, models, and semantic theories of concurrent, distributed, mobile, global-computingsystems; languages, security and types for global computing.=20 The workshop proceedings will be published in the ENTCS series and a selection of papers will appear in a special issue of the Journal of Theoretical Computer Science. It will be held as a ICALP2002 satellite event under the auspices of the EATCS.=20 Invited Speakers * Mart=EDn Abadi (UC Santa Cruz) * Luca Cardelli (Microsoft) * Matthew Hennessy (Sussex) * Jim Waldo (SUN Microsystems) Programme Committee * C=E9dric Fournet (Microsoft) * Andrew Gordon (Microsoft) * Alan Jeffrey (De Paul, Chicago) * Ugo Montanari (Pisa) * Catuscia Palamidessi (PennState) * Benjamin Pierce (UPenn) * Davide Sangiorgi (INRIA) * Vladimiro Sassone (Sussex, chair) * Peter Sewell (Cambridge) Important Dates Submission 29 Mar 2002 Notification 18 Jun 2002 PreFinal version 1 Jul 2002 Final version 31 Jul 2002 Submissions Authors are invited to submit an extended abstract of their papers, presenting original contributions to the workshop themes. Submissions should be in English and not exceed 15 standard pages. They should be sent as PS or PDF files to fwan@cogs.susx.ac.uk and be accompanied by a text-only message containing: title, abstract and keywords, the authors' full names, and address and e-mail for correspondence.=20 Simultaneous submission to other meetings with published proceedings is not allowed. =20 Organising Committee * Inmaculada Fortes Ruiz, Llanos Mora, Rafael Morales, Francisco Triguero (M=E1laga)=20 Sponsors The workshop will be held under the auspices of EATCS, the European Association of Theoretical Computer Science.=20 28-Jan-2002 11:32:35 -0400,2704;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 28 Jan 2002 11:32:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VDig-00001Z-00 for categories-list@mta.ca; Mon, 28 Jan 2002 11:29:20 -0400 Date: Mon, 28 Jan 2002 08:46:29 +0100 (CET) From: "Martin Markl, Mathematical Institute of the Academy" To: categories@mta.ca Subject: categories: Re: Operads In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk PROPs invented by Mac Lane in the 1960 do the job; operad is then a special case of a PROP. For example, Hopf algebras and various other bialgebras are described by PROPs. I believe you can find more details in @article{maclane:BAMS65, author={S. {Mac~Lane}}, title={Categorical Algebra}, journal={Bull. Amer. Math. Soc.}, year=1965, volume=71, pages={40--106}} There is also a more special notion called bioperad introduced recently by Wee Liang Gan - see his paper math.QA/0201074 posted on xxx.lanl.gov. Sincerely, Martin > Date: Mon, 19 Nov 2001 09:56:13 -0000 > From: S.J.Vickers@open.ac.uk > To: categories@mta.ca > Cc: univalg@yahoogroups.com > Subject: categories: Operads > > There's some discussion on the Universal Algebra list at present on operads. > > I'm not very familiar with them. What I understand from the discussion is > they capture single sorted algebraic theories with respect to a symmetric > monoidal product ox. For each natural number n an object of n-ary operators > O_n is given, and an algebra A has operations O_n ox A^(n) -> A where A^(n) > is A ox ... ox A n times. > > If you do this sort of thing with respect to categorical product, then it > already contains the information of the Lawvere theory category (for > single-sorted finitary algebraic theories), since hom(m,n) is hom(m,1)^n and > you take hom(m,1) to be O_m. But with a monoidal product this doesn't work. > It seemed to me that for proper generality the operad ought to have objects > O_mn (m, n natural numbers) representing the object of operations from A^(m) > to A^(n). Is there a name for that? > > Steve Vickers > Department of Pure Maths > Faculty of Maths and Computing > The Open University > ----------- > Tel: 01908-653144 > Fax: 01908-652140 > Web: http://mcs.open.ac.uk/sjv22 > > > > > 29-Jan-2002 08:18:52 -0400,3550;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jan 2002 08:18:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VXC0-0007A2-00 for categories-list@mta.ca; Tue, 29 Jan 2002 08:16:52 -0400 Date: Mon, 28 Jan 2002 09:17:52 -0500 (Eastern Standard Time) From: Walter Tholen To: categories@mta.ca Subject: categories: Galois and Hopf 2002 Message-ID: X-X-Sender: tholen@pascal.math.yorku.ca MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk SECOND ANNOUNCEMENT Dear Colleagues: This is a call for contributed talks to the "Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories" to be held September 23-28, 2002, at the Fields Institute in Toronto. http://www.fields.utoronto.ca/programs/scientific/02-03/galois_and_hopf/ See also below for a list of confirmed speakers. The program of the workshop will commence on Monday September 23, at 9am and run until noon Saturday September 28. In addition to the 20 invited lectures we expect to be able to place up to 30 contributed 20-minute talks in the program. CALL FOR PAPERS We invite you to submit an abstract by 15 May 2002, to be sent directly to all three organizers as a ps- or pdf-file or as a plain message. Notification of acceptance will be given by 15 June 2002. Please email abstracts to all: George Janelidze (george_janelidze@hotmail.com) Bodo Pareigis (pareigis@rz.mathematik.uni-muenchen.de) Walter Tholen (tholen@mathstat.yorku.ca) We plan to edit conference proceedings. Details will be communicated in the third announcement, to be sent in June. There will also be a poster session at the conference. If you are interested in presenting a poster, please notify the organizers, preferably by 15 May 2002. REGISTRATION Registration will be open in early 2002. The conference fee for all participants of the workshop is $130 (CDN), students $65 (CDN). The fee will include an excursion to the Niagara peninsula (planned for Wednesday, September 25 afternoon) and the conference dinner (planned for Thursday September 26). The fee for accompanying guests is $130. To be informed of when registration is open please contact programs@fields.utoronto.ca All participants (including invitees) are requested to register. HOUSING Participants should also arrange for their accommodation. Since tourism is still very active in Toronto during late summer/early fall, we advise to make reservations early; there is a link to a list of conveniently located hotels and guest houses from the site given above. We hope to welcome you at the workshop. George Janelidze, Bodo Pareigis, Walter Tholen Confirmed speakers (as of 25 January 2002): Francis Borceux, Univ. Catholique de Louvain, Belgium Dominique Bourn, Univ. Littoral, France Ronnie Brown, Univ. of Wales, UK Stefaan Caenepeel, Vrije Univ. of Brussels, Belgium Johannes Huebschmann, Univ. de Lille, France Max Kelly, Univ. of Sydney, Australia F.W. Lawvere, Univ. of New York at Buffalo, USA Andy Magid, Univ. of Oklahoma, USA Robert Pare', Dalhousie Univ., Canada Peter Schauenburg, Univ. of Munich, Germany Ross Street, Macquarie Univ., Australia Mitsuhiro Takeuchi, Univ. of Tsukuba Sakura-Mura, Japan Myles Tierney, Rutgers Univ., USA 29-Jan-2002 08:18:56 -0400,2696;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jan 2002 08:18:56 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VXCq-0007E7-00 for categories-list@mta.ca; Tue, 29 Jan 2002 08:17:44 -0400 From: david carlton MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15445.50477.270916.554411@jackfruit.Stanford.EDU> Date: Mon, 28 Jan 2002 13:39:57 -0800 To: categories@mta.ca Subject: categories: colimits of categories X-Mailer: VM 7.00 under 21.4 (patch 6) "Common Lisp" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Is there a good reference for the construction of colimits of categories? Here, by 'categories', I mean 1-categories; and I'm considering 1Cat as a weak 2-category. I've been playing around with this for the last week; I can construct limits without much trouble (at least if the index category is a 1-category; I assume that changing the index category to a 2-category wouldn't cause any substantial problems), but constructing colimits seems noticeably messier. It's not too bad if your index category is filtered, but in general it seems like a pain. I frequently see statements like 'nCat is expected to have all limits and colimits', so I assume that this has been verified in the case of n=1 somewhere. Also, while I'm asking, does the decategorification operation (from nCat into (n-1)Cat) commute with colimits? I was somewhat surprised to see that decategorification from 1Cat into 0Cat does commute with filtered colimits; so I'm wondering to what extent that statement generalizes. I.e. can I replace 1Cat by nCat, can I remove the word 'filtered', and for that matter can I replace colimits by limits? (I know decategorification doesn't commute with arbitrary limits of 1Cats - indeed, that's arguably where much of the fun of higher category theory comes into play - though I haven't thought too much about whether or not it commutes with filtered limits.) I have reason to hope that decategorification doesn't commute with filtered colimits of 2-categories, but no hard evidence; trying to check that seems like enough of a pain that I'm hoping somebody else has done it first. I haven't thought much about non-filtered colimits since I can't even construct them; I'd be surprised offhand if decategorification commuted with arbitrary colimits. Then again, I was surprised to see that it commuted with filtered colimits, so clearly my intuition isn't the most reliable guide in this case. David Carlton carlton@math.stanford.edu 29-Jan-2002 20:56:41 -0400,2784;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jan 2002 20:56:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16ViuC-0005np-00 for categories-list@mta.ca; Tue, 29 Jan 2002 20:47:16 -0400 Message-ID: <3C569ADF.1010602@tzi.de> Date: Tue, 29 Jan 2002 13:51:43 +0100 From: Lutz Schroeder User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:0.9.4) Gecko/20010923 X-Accept-Language: en-us MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: colimits of categories References: <15445.50477.270916.554411@jackfruit.Stanford.EDU> Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk > Is there a good reference for the construction of colimits of > categories? > Here, by 'categories', I mean 1-categories; and I'm considering > 1Cat as a weak 2-category. I've been playing around with this for > the last week; I can construct limits without much trouble (at > least if the index category is a 1-category; I assume that changing > the index category to a 2-category wouldn't cause any substantial > problems), but constructing colimits seems noticeably messier. > It's not too bad if your index category is filtered, but in general > it seems like a pain. The construction of quotients of 1-categories (which, together with coproducts, make up arbitrary colimits) is indeed somewhat messy: the naive quotient (equivalence classes of objects and morphisms) forms a graph with a partial composition operation that obeys the identity law but no further axioms. Over this structure, one can construct a free category (the category of paths, modulo the smallest congruence that makes the quotient map a functor), which is, then, the actual quotient category; which equivalence classes of arrows are or are not identified in the quotient category is, in the general case, hard to predict. References include M. Bednarczyk, M. Borzyszkowski, and W. Pawlowski: Generalized congruences --- epimorphisms in Cat. Theory and Applications of Categories 5 (1999), 266-280 L. Schroeder and H. Herrlich: Free adjunction of morphisms. Applied Categorical Structures 8 (2000), 595-606. Greetings, Lutz -- ----------------------------------------------------------------------------- Lutz Schroeder Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3054 University of Bremen lschrode@informatik.uni-bremen.de P.O.Box 330440, D-28334 Bremen http://www.informatik.uni-bremen.de/~lschrode ----------------------------------------------------------------------------- 29-Jan-2002 20:56:44 -0400,3194;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jan 2002 20:56:44 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16ViwZ-00063s-00 for categories-list@mta.ca; Tue, 29 Jan 2002 20:49:43 -0400 Date: Tue, 29 Jan 2002 16:00:21 +0100 (CET) From: "Martin Markl, Mathematical Institute of the Academy" To: categories@mta.ca Subject: categories: Re: Operads Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Peter May asked me to send in a correction of my message enclosed below; he says that PROPs were invented in unpublished joint work of Adams and Mac Lane, not Mac Lane alone. ---------- Forwarded message ---------- Date: Mon, 28 Jan 2002 08:46:29 +0100 (CET) From: "Martin Markl, Mathematical Institute of the Academy" To: categories@mta.ca, S.J.Vickers@open.ac.uk Cc: Steve Shnider , JAMES STASHEFF Subject: Re: categories: Operads (fwd) Dear Steve Vickers PROPs invented by Mac Lane in the 1960 do the job; operad is then a special case of a PROP. For example, Hopf algebras and various other bialgebras are described by PROPs. I believe you can find more details in @article{maclane:BAMS65, author={S. {Mac~Lane}}, title={Categorical Algebra}, journal={Bull. Amer. Math. Soc.}, year=1965, volume=71, pages={40--106}} There is also a more special notion called bioperad introduced recently by Wee Liang Gan - see his paper math.QA/0201074 posted on xxx.lanl.gov. Sincerely, Martin > Date: Mon, 19 Nov 2001 09:56:13 -0000 > From: S.J.Vickers@open.ac.uk > To: categories@mta.ca > Cc: univalg@yahoogroups.com > Subject: categories: Operads > > There's some discussion on the Universal Algebra list at present on operads. > > I'm not very familiar with them. What I understand from the discussion is > they capture single sorted algebraic theories with respect to a symmetric > monoidal product ox. For each natural number n an object of n-ary operators > O_n is given, and an algebra A has operations O_n ox A^(n) -> A where A^(n) > is A ox ... ox A n times. > > If you do this sort of thing with respect to categorical product, then it > already contains the information of the Lawvere theory category (for > single-sorted finitary algebraic theories), since hom(m,n) is hom(m,1)^n and > you take hom(m,1) to be O_m. But with a monoidal product this doesn't work. > It seemed to me that for proper generality the operad ought to have objects > O_mn (m, n natural numbers) representing the object of operations from A^(m) > to A^(n). Is there a name for that? > > Steve Vickers > Department of Pure Maths > Faculty of Maths and Computing > The Open University > ----------- > Tel: 01908-653144 > Fax: 01908-652140 > Web: http://mcs.open.ac.uk/sjv22 > > > > > 29-Jan-2002 20:56:48 -0400,2378;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jan 2002 20:56:47 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Viza-0006qX-00 for categories-list@mta.ca; Tue, 29 Jan 2002 20:52:50 -0400 User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.02.2022 Date: Wed, 30 Jan 2002 10:45:46 +1100 Subject: categories: Re: colimits of categories From: Michael Batanin To: Message-ID: In-Reply-To: <15445.50477.270916.554411@jackfruit.Stanford.EDU> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk In a paper by M.Kelly `A unified treatment of transfinite construction for free algebras, free monoids, colimits, associated sheaves, and so on', Bull. of the Australian Math. Soc., 22 (1980), 1-85. there is a general construction of colimits in the category of algebras of a finitary monad. The category of 1-Cat is an algebra of a free category on graph monad, which is finatary so the colimits exist in 1-Cat. Informally what we have to do to construct a coequalizer in 1-Cat is the following. First we have to construct a corresponding coequalizer in graphs. Then apply free category functor to it and form another coequaliser in graphs. This process continuing. Finally we have a sequence of graphs and its colimit is our coequalizer in 1-Cat. The same argument show the existence of colimits in n-Cat (strict n-categories and strict n-functor) or weak n-Cat with strict n-functors (if you accept my definition of weak n-catgory introduced in 'Monoidal globular categories as a natural environment for the theory of weak $n$-categories', Adv. Math. 136 (1998), pp. 39-103.). If we think of n-Cat as a category of algebras over an appropriate n-operad then it contains a full subcategory of algebras such that their underlying n-graphs (n-globular sets in other terminology) are discretes in dimension n (i.e. Hom(a,b) = 0 if a /ne b and Hom(a,a)=1). This subcategory is closed under limits and so we have a left adjoint from n-Cat to this subcategory which can be considered as a decategorification functor. Therefore, it commutes with colimits. Michael Batanin. 29-Jan-2002 20:56:51 -0400,1875;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jan 2002 20:56:51 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Viut-0004yQ-00 for categories-list@mta.ca; Tue, 29 Jan 2002 20:47:59 -0400 Message-ID: From: S.J.Vickers@open.ac.uk To: categories@mta.ca Subject: categories: Re: colimits of categories Date: Tue, 29 Jan 2002 14:08:55 -0000 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2653.19) Content-Type: text/plain; charset="iso-8859-1" Sender: cat-dist@mta.ca Precedence: bulk David Carlton asks - > Is there a good reference for the construction of colimits of > categories? If I remember correctly, Philip Higgins's little book "Notes on categories and groupoids" (Van Nostrand Reinhold 1971) is good on that kind of thing. You're right that the non-filtered colimits are distinctly messier than the limits. There are two reasons. The first is that that is the way of algebra anyway - think of colimits of monoids or groups, for instance. Universal algebra says that colimits exist for every algebraic theory, but the construction is intricate. You first make an algebra of all possible terms (expressions) and then factor out a congruence to enforce the equational laws and the cocone commutativities. The second reason is that categories are models not of an algebraic theory, but of an essentially algebraic theory (some operations - specifically here composition - are only partial, with domain of definition stipulated equationally). The techniques of universal algebra still work, by and large, but the proof is even more intricate than the 2-step process in algebra. This is because imposing equations can cause new terms to spring into existence. Steve Vickers. 30-Jan-2002 08:58:25 -0400,2955;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 08:58:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuG2-0001CV-00 for categories-list@mta.ca; Wed, 30 Jan 2002 08:54:34 -0400 X-Authentication-Warning: spurv.itu.dk: birkedal set sender to birkedal@itu.dk using -f To: categories@mta.ca Subject: categories: CFP: Domain Theory Workshop in Honour of Dana Scott's 70'th Message-Id: From: cat-dist@mta.ca Date: Wed, 30 Jan 2002 08:54:34 -0400 birthday Reply-To: birkedal@itu.dk Content-Type: text/plain; charset=US-ASCII From: Lars Birkedal Date: 28 Jan 2002 11:42:06 +0100 Message-ID: Lines: 55 User-Agent: Gnus/5.0807 (Gnus v5.8.7) XEmacs/21.1 (Cuyahoga Valley) MIME-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk Call for Papers to Workshop on Domain Theory in Honour of Dana S. Scott's 70'th birthday. July 20-21, 2002 Affiliated with FLoC'02 http://www.it-c.dk/research/theory/scott-fest-2002/ This workshop on Domain Theory is held in honour of Dana Scott's 70'th birthday. The workshop is aimed at computer scientists and mathematicians who share an interest in the mathematical foundations of computer science. The workshop will focus on domains, their applications, and closely related topics. Contributions establishing connections to logic, type theory, recursion theory, and topology are welcome. Contributions on applications of domains in semantics etc. are also very welcome. The workshop will have invited talks and contributed research talks of 30 minutes each. Invited Speakers: Pierre-Louis Curien, CNRS, Universite Paris 7 Martin Hyland, University of Cambridge Gordon Plotkin, University of Edinburgh John C. Reynolds, Carnegie Mellon University Viggo Stoltenberg-Hansen, University of Uppsala (provisional) Glynn Winskel, University of Cambridge (provisional) Submission Procedure: Researchers are invited to submit an extended abstract of at most 10 pages by sending an e-message containing the postscript file to birkedal@it-c.dk or by mailing a copy to Lars Birkedal The IT University of Copenhagen Glentevej 67 DK-2400 Copenhagen NV DENMARK before April 15, 2002. Authors will be notified of acceptance by May 31, 2002. Proceedings: We expect the invited and contributed papers will be published in ENTCS and available for the workshop. We also expect to edit a special issue of a major scientific journal. Organizers: Lars Birkedal, birkedal@it-c.dk Giuseppe Rosolini, rosolini@disi.unige.it The workshop is supported in part by: The Theory Deparment at the IT University of Copenhagen 30-Jan-2002 08:59:57 -0400,7377;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 08:59:57 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuJs-00009V-00 for categories-list@mta.ca; Wed, 30 Jan 2002 08:58:32 -0400 Message-ID: <3C554D77.72119B5@csc.liv.ac.uk> Date: Mon, 28 Jan 2002 13:09:11 +0000 From: Peter McBurney X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.4.9-12 i686) X-Accept-Language: en MIME-Version: 1.0 To: CATEGORIES LIST Subject: categories: CFP: Visual Representations and Interpretations Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-MIME-Autoconverted: from 8bit to quoted-printable by ribble.server.csc.liv.ac.uk id NAA02217 Sender: cat-dist@mta.ca Precedence: bulk WITH APOLOGIES FOR MULTIPLE POSTINGS SECOND CALL FOR PAPERS 2nd International Conference on VISUAL REPRESENTATIONS AND INTERPRETATIONS Liverpool, UK, September 9 - 12, 2002 Web-Page: http://www.csc.liv.ac.uk/~vri2/ Contributions are invited for a multi-disciplinary workshop on Visual Representations and Interpretations. This will be a multi-disciplinary meeting exploring all aspects of visual images, their interpretation, representation and modeling, and their relationships to other forms of human knowledge and activities. SCOPE AND AIMS OF THE WORKSHOP The value of multi-disciplinary research, the exchanging of ideas and methods across traditional discipline boundaries, is well recognised.=20 It could be argued that many of the advances in science and engineering take place because the ideas, methods and the tools of thought from one discipline become re-applied in others. The topic of "the visual" has become increasingly important as advances in technology have led to multi-media and multi-modal representations, and extended the range and scope of visual representation and interpretation in our lives. Under this broad heading there are many different perspectives and approaches, from across the entire spectrum of human knowledge and activity. The development of advanced graphics for computer games and film animations, for example, has drawn on and led developments in computational geometry. Even outside the technological sphere, recent controversies over artworks which some have considered to be blasphemous show the power of the visual to manifest wildly different interpretations, and to become a topic of everyday conversation and a focus of political activity. One goal of this workshop on Visual Representations and Interpretations is to break down cross-disciplinary barriers, by bringing together people working in a wide variety of disciplines where visual representations and interpretations are exploited. The first Workshop on Visual Representations and Interpretations was held in Liverpool in 1998. Contributions to the workshop came from researchers actively investigating visual representations and interpretations in a wide variety of areas including: art, architecture, biology, chemistry, clinical medicine, cognitive science, computer science, education, engineering, graphic design, linguistics, mathematics, philosophy, physics, psychology and social science. VRI2002 aims to build on this good beginning, and to provide a forum for wide-ranging and multi-disciplinary discussion on visual representations and interpretations. Contributions on any aspect of visual representations and interpretations are welcomed, including, though of course not limited to: - visual representation languages - film and photographic interpretation - art as argument - diagrams and sketches - the philosophy, sociology and politics of art and images - formalization and representation of images - visual human-machine interaction - connections between visual and other human senses - computational geometry - diagrammatic reasoning - the modeling of patterns and form - blueprints and scale models - visual metaphors and knowledge discovery SUBMISSIONS Contributions in the form of original research papers are invited. Papers should be a maximum of 12 pages in length. There will be the opportunity to edit accepted papers after the Workshop for inclusion in the final published proceedings. Paper submissions should be sent to: Grant Malcolm (Conference Chair) Department of Computer Science University of Liverpool Chadwick Building Peach Street Liverpool L69 7ZF UK Papers can also be submitted by email, PROVIDED THEY ARE IN PDF OR POSTSCRIPT FORMAT,in which case they can be sent to: grant@csc.liv.ac.uk IMPORTANT DATES Submission of contributions: 1 April 2002 Notification of Acceptance: 15 May 2002 Submission deadline for pre-proceedings: 20 July 2002 VRI-2002 Conference: 9-12 September 2002 Submission deadline for Elsevier volume: 30 September 2002 The edited proceedings of the workshop will be published after the event by Elsevier Science in a volume entitled "Multidisciplinary Studies of Visual Representations and Interpretations" Submissions will be refereed by two or more members of the Program Committee: PROGRAMME COMMITTEE Caroline Baillie (Liverpool, UK) Michael Biggs (Hertfordshire, UK) Ernst Binz (Mannheim, Germany) Nicola Dioguardi (Milan, Italy) Andr=E9e Ehresmann (Amiens, France) Paul Fishwick (Gainesville, USA) Jean-Louis Giavitto (Evry, France) Peter Giblin (Liverpool, UK) Joseph Goguen (San Diego, USA) David Goodsell (La Jolla, USA) Leo Groarke (Waterloo, Canada) Rom Harr=E9 (Oxford, UK, and Washington, USA) Robin Hendry (Durham, UK) Mike Holcombe (Sheffield, UK) John Lee (Edinburgh, UK) Deborah Leishman (Los Alamos, USA) Charles Lund (Newcastle, UK) Michael Leyton (New York, USA) Peter McBurney (Liverpool, UK) Grant Malcolm (Liverpool, UK) Mary Meyer (Los Alamos, USA) Arthur Miller (London, UK)=20 Irene Neilson (Liverpool, UK) Ray Paton (Liverpool, UK)=20 Walter Schempp (Seigen, Germany) Travel and accommodation details will be posted in due course on the conference web-page: http://www.csc.liv.ac.uk/~vri2/ =20 Questions and inquiries should be directed to: Ray Paton Department of Computer Science University of Liverpool Email: R.C.Paton@csc.liv.ac.uk **************************************************************** =20 Peter McBurney =20 Department of Computer Science =20 University of Liverpool =20 Liverpool L69 7ZF =20 U.K. =20 =20 Tel: + 44 151 794 6760 Email: P.J.McBurney@csc.liv.ac.uk =20 Web page: www.csc.liv.ac.uk/~peter/ =20 = =20 **************************************************************** 30-Jan-2002 09:01:47 -0400,5321;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 09:01:47 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuLe-0008Bn-00 for categories-list@mta.ca; Wed, 30 Jan 2002 09:00:22 -0400 From: Steve Lack MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15447.22138.158932.645946@milan.maths.usyd.edu.au> Date: Wed, 30 Jan 2002 13:12:10 +1100 To: categories@mta.ca Subject: categories: Re: colimits of categories X-Mailer: VM 6.90 under 21.1 (patch 7) "Biscayne" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk David Carlton writes about colimits of categories. Other people have answered many of his questions, but not yet: > > Also, while I'm asking, does the decategorification operation (from > nCat into (n-1)Cat) commute with colimits? I was somewhat surprised > to see that decategorification from 1Cat into 0Cat does commute with > filtered colimits; so I'm wondering to what extent that statement > generalizes. I.e. can I replace 1Cat by nCat, can I remove the word > 'filtered', and for that matter can I replace colimits by limits? (I > know decategorification doesn't commute with arbitrary limits of 1Cats > - indeed, that's arguably where much of the fun of higher category > theory comes into play - though I haven't thought too much about > whether or not it commutes with filtered limits.) If by n-Cat you mean strict n-categories and strict n-functors, then here is a response to the ``colimit'' part of the question. First of all, you can't generalize from filtered colimits to arbitrary colimits, even in the case 1Cat-->0Cat. Write Cat for 1Cat and Set for 0Cat, and P:Cat-->Set for the decategorification functor, which sends a category to its set of isomorphism classes of objects. This functor P preserves filtered colimits, as you said (or see below), and clearly also preserves coproducts, but doesn't preserve the coequalizer f q A ----> B ----> C ----> g where C is the free-living isomorphism, with objects 0 and 1, and two mutually inverse non-identity arrows 0-->1 and 1-->0; where B has objects 0 and 1, and arrows freely generated by 0-->1 and 1-->0, and where q is the evident quotient; where A has two objects 0 and 1 and arrows freely generated by 0-->0 and 1-->1, and where f and g are the evident functors. Alternatively, observe that Cat is locally finitely presentable (lfp), so that if it preserved all colimits it would have a right adjoint, and prove that it does not have one. On the other hand, decategorification P:n-Cat-->(n-1)-Cat does preserve filtered colimits for any n. To see this, write n-Catg for the full subcategory of n-Cat consisting of those n-categories in which all n-cells are invertible. The inclusion I:n-Catg --> n-Cat has a right adjoint R which forgets all non-invertible n-cells. (It also has a left adjoint.) Now RI=1 and PIR=P, so that P will preserve filtered colimits if PI and R do so. But PI:n-Catg ---> (n-1)-Cat has a right adjoint D, which regards an (n-1)-category as an n-category with no non-identity n-cells. Thus PI preserves all colimits, and P will preserve filtered colimits provided R does so. If V is locally finitely presentable, then so is V-Cat [G.M.Kelly and Stephen Lack, V-Cat is locally presentable or locally bounded if V is so, Theory Appl. Cat. 8:555-575, 2001]. From the equation (n+1)-Cat=(n-Cat)-Cat and the fact that 0-Cat(=Set) is lfp, it follows by induction that n-Cat is lfp for every n. Similarly from the equation (n+1)-Catg=(n-Catg)-Cat and that fact that 1-Catg(= the category Gpd of groupoids) is lfp, it follows that n-Catg is lfp for every n. Now R:n-Cat-->n-Catg is a right adjoint functor between lfp categories, so will preserve filtered colimits if and only if its left adjoint I:n-Catg-->n-Cat preserves finitely presentable objects. For an object G of V, write 2_G for the V-category with objects 0 and 1, and homs 2_G(0,0)=2_G(1,1)=I, 2_G(1,0)=0, and 2_G(0,1)=G. By the Kelly-Lack paper, the finitely presentable objects of V-Cat are the closure under finite colimits of the V-categories of the form 2_G for G a finitely presentable object of V. It follows that I:(n+1)-Catg --> (n+1)-Cat will preserve finitely presentable objects if I:n-Catg ---> n-Cat does so. Thus it remains only to show that I:Gpd-->Cat preserves finitely presentable objects, or equivalently that R:Cat-->Gpd preserves filtered colimits. There are various ways to do this. One could use the description of filtered colimits in Cat given in the Kelly-Lack paper to show that IR preserves filtered colimits, and deduce that R does so. Alternatively one could show that the ``free-living isomorphism'' (called C above) is finitely presentable in both Gpd and Cat, and constitutes a strong generator of Gpd, and deduce that I preserves finitely presentable objects. Similarly, P:n-Cat-->(n-1)-Cat will preserve whatever limits PI preserves, and once again an inductive argument shows that PI will preserve whatever limits PI:Gpd-->Set preserves (products, for instance). Steve Lack. 30-Jan-2002 09:02:37 -0400,2558;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 09:02:37 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuMT-0001SM-00 for categories-list@mta.ca; Wed, 30 Jan 2002 09:01:13 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Tue, 29 Jan 2002 21:21:00 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: colimits of categories In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Steve is right about the messiness. The very first paper I am aware of on the subject used 25 pages of detailed computations to show that the amalgamated sum of two categories gotten by identifying a single object of one category with an object of the other exists. That must have been sometime in the 60s. What a mess! A good mathematician, whom I won't embarrass by identifying. Michael On Tue, 29 Jan 2002 S.J.Vickers@open.ac.uk wrote: > David Carlton asks - > > Is there a good reference for the construction of colimits of > > categories? > > If I remember correctly, Philip Higgins's little book "Notes on categories > and groupoids" (Van Nostrand Reinhold 1971) is good on that kind of thing. > > You're right that the non-filtered colimits are distinctly messier than the > limits. There are two reasons. > > The first is that that is the way of algebra anyway - think of colimits of > monoids or groups, for instance. Universal algebra says that colimits exist > for every algebraic theory, but the construction is intricate. You first > make an algebra of all possible terms (expressions) and then factor out a > congruence to enforce the equational laws and the cocone commutativities. > > The second reason is that categories are models not of an algebraic theory, > but of an essentially algebraic theory (some operations - specifically here > composition - are only partial, with domain of definition stipulated > equationally). The techniques of universal algebra still work, by and large, > but the proof is even more intricate than the 2-step process in algebra. > This is because imposing equations can cause new terms to spring into > existence. > > Steve Vickers. > > > 30-Jan-2002 09:03:32 -0400,3062;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 09:03:32 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuNL-0001CW-00 for categories-list@mta.ca; Wed, 30 Jan 2002 09:02:07 -0400 Date: Wed, 30 Jan 2002 07:34:44 +0100 Message-Id: <200201300634.HAA29014@chtapach.loria.fr> From: Christophe Ringeissen To: categories@mta.ca Subject: categories: AMAST'2002 **** NEW EXTENDED DEADLINE **** X-Mailer: VM 6.75 under 21.1 (patch 14) "Cuyahoga Valley" XEmacs Lucid Reply-To: Christophe.Ringeissen@loria.fr Sender: cat-dist@mta.ca Precedence: bulk [Apologies for multiple copies] AMAST'2002 **** NEW EXTENDED DEADLINE: FEBRUARY 15, 2002 **** In response to multiple requests, the submission deadline is extended until FEBRUARY 15, 2002 ---------------------------------------------------------------------------- AMAST 2002 CALL FOR PAPERS 9-th International Conference on Algebraic Methodology And Software Technology AMAST 2002, September 9-13, 2002 St. Gilles les Bains, Reunion Island, France * Important Dates: Paper submissions February 15, 2002 (EXTENDED DEADLINE) Notification of paper acceptance April 27, 2002 Camera ready papers June 1, 2002 AMAST 2002 conference September 9-13, 2002 * Topics: As in previous years, we invite papers reporting original research on setting software technology on a firm mathematical basis. Of particular interest is research on using algebraic, logic, and other formalisms suitable as foundations for software technology, as well as software technologies developed by means of logic and algebraic methodologies. * Submissions: We invite prospective authors to submit electronically previously unpublished papers of high quality. Papers must be no longer than 15 pages (6 pages for system demonstrations) and should be prepared using LaTeX and the LNCS style that can be downloaded from the URL: http://www.springer.de/comp/lncs/authors.html Please send a fully self-contained PostScript file to amast@loria.fr As in the past, the AMAST'2002 proceedings will be published by Springer-Verlag in the Lecture Notes in Computer Science Series. * Program Committee: V.S. Alagar, E. Astesiano, M. Bidoit, D. Bolignano, M. Broy, J. Fiadeiro, B. Fischer, K. Futatsugi, A. Haeberer, N. Halbwachs, A. Haxthausen, D. Hutter, P. Inverardi, B. Jacobs, M. Johnson, H. Kirchner (PC chair), P. Klint, T. Maibaum, Z. Manna, J. Millen, P. Mosses, F. Orejas, R. de Queiroz, T. Rus, C. Ringeissen (PC chair assistant), D. Sannella, P.-Y. Schobbens, G. Scollo, A. Tarlecki, M. Wirsing * Local Organization Chair: Teodor Knapik, Univ. de la Reunion * Further information: For regularly updated details of the conference organization send email to amast@loria.fr or visit the AMAST'2002 web page: http://www.loria.fr/conferences/amast2002 30-Jan-2002 09:06:02 -0400,4748;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 09:06:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuPj-0001gb-00 for categories-list@mta.ca; Wed, 30 Jan 2002 09:04:35 -0400 Message-ID: <004601c1a97a$b03a4e80$fb50883e@brown1> From: "Ronald Brown" To: References: Subject: categories: Re: colimits of categories Date: Wed, 30 Jan 2002 10:40:43 -0000 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Sender: cat-dist@mta.ca Precedence: bulk reply to r.brown@bangor.ac.uk Another paper to look up is by Philip Higgins in Mathematische Nachrichten 27 (1963) 115-132 which generalised his earlier work on algebras with a scheme of operators to partially defined operators. One way of looking at this is that a morphism f: C \to D of categories (or groupoids) may identify objects. So one thing to do is factorize it through through a universal morphism which does just that identification (compare Steve Vickers' comments). Philip's book (in fact his 1964 paper on presentations of groups) shows how you thereby get free groupoids on graphs and free products of groups from one construction. An advantage of this is you need only one normal form theorem, whereas the group theory books give two proofs. There is a paper by M.Zisman looking at the effect of this particular construction on classifying spaces of categories and groupoids. This is seen as a `change of base' construction (a favourite notion of Grothendieck) in my paper ``Homotopy theory, and change of base for groupoids and multiple groupoids'', {\em Applied categorical structures}, 4 (1996) 175-193. This also relates change of base to results in algebraic topology such as n-adic excision and Hurewicz theorems. The n-adic theorems were found via this route (n=2 is the well known relative case). In homotopy theory one would like to know what happens to a homotopy type if you change its lower dimensional part. An algebraic solution to this would also give the homotopy types of spheres, since S^n is obtained from a disc E^n by shrinking the boundary S^{n-1} to a point. So we can't expect a calculable solution overnight! In the strict multiple groupoid case some explicit calculations have been done (using crossed n-cubes of groups, Ellis-Steiner) , but all this suggests the interesting difficulty of calculating with multiple categories. On the other hand, calculating with groups is not a walk-over either, and the expectation is that some group theory results are best understood from a higher dimensional viewpoint. For colimits of topological categories and groupoids see also (with J.P.L. HARDY), ``Topological groupoids I: universal constructions'', {\em Math. Nachr.} 71 (1976) 273-286. which gets it from an adjoint functor type construction: this probably overlaps work of C. Ehresmann. Ronnie Brown ----- Original Message ----- From: To: Sent: Tuesday, January 29, 2002 2:08 PM Subject: categories: Re: colimits of categories > David Carlton asks - > > Is there a good reference for the construction of colimits of > > categories? > > If I remember correctly, Philip Higgins's little book "Notes on categories > and groupoids" (Van Nostrand Reinhold 1971) is good on that kind of thing. > > You're right that the non-filtered colimits are distinctly messier than the > limits. There are two reasons. > > The first is that that is the way of algebra anyway - think of colimits of > monoids or groups, for instance. Universal algebra says that colimits exist > for every algebraic theory, but the construction is intricate. You first > make an algebra of all possible terms (expressions) and then factor out a > congruence to enforce the equational laws and the cocone commutativities. > > The second reason is that categories are models not of an algebraic theory, > but of an essentially algebraic theory (some operations - specifically here > composition - are only partial, with domain of definition stipulated > equationally). The techniques of universal algebra still work, by and large, > but the proof is even more intricate than the 2-step process in algebra. > This is because imposing equations can cause new terms to spring into > existence. > > Steve Vickers. > > > > 30-Jan-2002 09:06:16 -0400,3084;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 09:06:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16VuQx-0001lw-00 for categories-list@mta.ca; Wed, 30 Jan 2002 09:05:51 -0400 To: categories@mta.ca Subject: categories: bases for locally compact spaces Message-Id: From: Paul Taylor Date: Wed, 30 Jan 2002 11:58:50 +0000 X-Ident: pt Sender: cat-dist@mta.ca Precedence: bulk Bases for spaces Has anyone come across this was of seeing locally compact spaces? We say that a system B_n of VECTORS in a VECTOR SPACE is a BASIS if any other vector U can be expressed as a sum of scalar multiples of basic vectors. Likewise, we say that a system B_n of OPEN SUBSETS of a TOPOLOGICAL SPACE is a BASIS if any other open set U can be expressed as a "sum" (disjunction) of basic opens. How do we find out which basis elements contribute to the sum, and by what scalar multiple? By applying the DUAL BASIS A_n to the given element U, ie A_n.U Then U = sum_n A_n.U * B_n where - "sum" means linear sum, disjunction or existential quantification, - "scalars" in the case of topology range over the Sierpinski space, - the dot denotes - inner product of a dual vector with a vector to yield a scalar, - that U is an element of the family A_n, or - lambda application, - `*' denotes multiplication by a scalar or a vector, or conjunction. In topology, each A_n is a Scott-open family of open subsets. Unfortunately, in general it need not be a filter. In the case where it is a filter, it corresponds by the Hofmann--Mislove theorem to a compact saturated subspace K_n. Then if A_n.U is true, B_n < K_n < U where < denotes non-strict subset inclusion. In this case K_n provides a basis of compact neighbourhoods. Anyway, if A_n.B_n is true then B_n is itself compact open, and more generally A_n.U implies B_n << U ("way below"). Thus, A_n.U is defined in terms of - the traditional definition of local compactness as the existence of a compact subspace between B_n and U - continuous lattices as B_n << U. As you might have guessed, I discovered this during my current work on domain theory in Abstract Stone Duality, and have lambda-terms for A_n and B_n. Indeed, if such a basis exists for a space X then X is a Sigma-split subspace of Sigma^N (in the sense of my recently-announced paper "Subspaces in Abstract Stone Duality"), where i: X -> Sigma^N by x |--> lambda n. B_n.x I: Sigma^X -> Sigma^2 N by U |--> lambda psi. some n. A_n.U * psi.n make Sigma^X a retract of Sigma^2 N. Conversely, given i and I,we define a basis indexed, not by numbers themselves, but by lists (k) of numbers, by B_k.x = all n in k. (i.x).n A_k.U = (I.U).(lambda n.n in k) Paul Taylor (no academic affiliation) ASD web page: http://www.dcs.qmul.ac.uk/~pt/ASD 30-Jan-2002 19:52:11 -0400,2568;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 19:52:11 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16W4TJ-0008Mt-00 for categories-list@mta.ca; Wed, 30 Jan 2002 19:48:58 -0400 Mime-Version: 1.0 X-Sender: street@hera.ics.mq.edu.au Message-Id: Date: Thu, 31 Jan 2002 10:10:32 +1100 To: categories@mta.ca From: Ross Street Subject: categories: Max Kelly recovering quickly Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Category Theorists may not know that Max Kelly had a heart operation last Friday (25 January 2002). He was given a sextuple bypass. I have heard today from Imogen Kelly that "Max was a lot brighter [yesterday] and is now doing everything by himself. He'll probably come home on Friday." Imogen's bulletin from Tuesday was as follows: ---------------------------------------------------------------- From: "Imogen Kelly" To: "'Ross Street'" Subject: RE: Max Date: Tue, 29 Jan 2002 22:09:21 +1100 X-Priority: 3 (Normal) Importance: Normal Status: Dear Ross, Thanks for your message. The operation itself went very well and, apparently, having six by-passes is a positive rather than a negative outcome. It means that there were six rather than a fewer number of arteries that were suitable sites for grafting, and the surgeon decided to do them all. We were warned that there would be wild mood swings after the operation and I guess (and hope) we've had them all. Max has been doped up to the eyeballs until this afternoon and already I can notice a big change now that he's off the morphine. Yes, the recuperation period will be slow. This afternoon, patients' carers attended a seminar where it was explained to us exactly what can and can't be done over the next six to eight weeks. Prolonged sitting and writing are both out, so I guess I'm going to be very unpopular as I enforce all the rules. The six-week period should be treated as holiday time while the sternum knits. Amazingly, Max and all the other patients who had surgery at the same time are walking. Because he was already unsteady on his pins and because of all the morphine he was taking, Max still needs some support when walking, but that will improve over the next few days. Regards, Imogen ---------------------------------------------------------------- Regards, Ross 30-Jan-2002 19:52:45 -0400,3105;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 19:52:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16W4Wg-0004M2-00 for categories-list@mta.ca; Wed, 30 Jan 2002 19:52:26 -0400 Content-Type: text/plain; charset="iso-8859-1" From: Carsten Butz Reply-To: butz@it-c.dk To: categories@mta.ca Subject: categories: PSSL 76 - Second Announcement Date: Wed, 30 Jan 2002 16:05:20 +0100 X-Mailer: KMail [version 1.2] MIME-Version: 1.0 Message-Id: <02013016052008.01063@vip164.it-c.dk> Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk PERIPATETIC SEMINAR ON SHEAVES AND LOGIC (PSSL 76) Second Announcement http://www.it-c.dk/research/theory/Seminars/pssl76.html Dear friends and colleagues, The 76th PSSL will be held at the IT-University of Copenhagen over the weekend 2-3 March, 2002. As usual we welcome talks on sheaves, category theory, logic, and related areas such as applications in (theoretical) computer science. As the meeting is informal in nature talks on work in progress are also welcome. Those interested in attending the meeting are kindly asked to complete the registration form below and return it to Carsten Butz (butz@it-c.dk) preferably before Monday, February 18. We maintain a webpage for this seminar at http://www.it-c.dk/research/theory/Seminars/pssl76.html which contains some travel information and details about accommodation. We suggest that you make a reservation at the following hotel: Leda Hotel Svanevej 6 2400 Copenhagen NV Tel: +45 35 83 12 22 Fax: +45 35 83 12 24 Email: leda@ledahotel.dk Payment: American Express, Cash, Check, Dankort, Diners Club, Eurocard, MasterCard, VISA Rate: DKK 600 (one Euro is about DKK 7.50) The hotel is in walking distance from the IT-University. Please mention that you will be visiting the IT-University to get the special rate of DKK 600. If your budget is tight the webpage suggests some other places further away where you might want to stay. If you need assistance or if you cannot access information on the webpage please do not hesitate to contact us at butz@it-c.dk. Looking forward to seeing you here in Copenhagen, Lars Birkedal (IT-C) Carsten Butz (IT-C, butz@it-c.dk) Thomas Hildebrandt (IT-C) Anders Kock (Aarhus University) ------------------------------------------------------- PSSL 76 Registration Form Name: Affiliation: Address: Email: I wish to attend the 76th meeting of the PSSL in Copenhagen. *I would like to give a talk entitled: *I have reserved accommodation on my own - at "Leda Hotel" for Friday/Saturday/Sunday night(s) - at another place (please specify) for Friday/Saturday/Sunday night(s) *Please reserve accommodation for me - at "Leda Hotel" for Friday/Saturday/Sunday night(s) - at another place (please specify) for Friday/Saturday/Sunday night(s) *Delete if inappropriate. 30-Jan-2002 19:55:13 -0400,4210;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jan 2002 19:55:13 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16W4Z5-000416-00 for categories-list@mta.ca; Wed, 30 Jan 2002 19:54:58 -0400 From: david carlton MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15448.18734.320960.116427@jackfruit.Stanford.EDU> Date: Wed, 30 Jan 2002 11:27:42 -0800 To: categories@mta.ca Subject: categories: Re: colimits of categories In-Reply-To: <15447.22138.158932.645946@milan.maths.usyd.edu.au> References: <15447.22138.158932.645946@milan.maths.usyd.edu.au> X-Mailer: VM 7.00 under 21.4 (patch 6) "Common Lisp" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Thanks for all the responses to my colimits question; I greatly appreciate them, and it will take me a while to digest them. I think I should be a bit more precise as to what I'm asking for, so let me try again: First, here's what I mean by a colimit of categories: let I be a 1-category, trivially extended to a weak 2-category with only identity 2-morphisms. (Or we could even have I be an arbitrary weak 2-category; I'm not too worried about that right now, but eventually I'd like an answer.) And let F be a weak functor from I to the 2-category 1Cat (which happens to be strict, but we think of it as a weak 2-cat.) Then: I want a 1-cat colim(F) such that, for all 1-cats C, the categories Hom_1Cat(colim(F),C) and Hom_(1Cat^I)(F,diag^I(C)) are equivalent, where by diag^I(C) I mean the constant functor from I to 1Cat^I sending all objects of I to C and all morphisms to identity morphisms. So I'm not looking at the set of functors from colim(F) to C: I don't really care whether or not that's equivalent to the set of functors from F to diag^I(C). I want an equivalence of categories. I'm fairly sure that some of the responses that I got answer this question; I'll look up the references and come back if I have more questions, but I'm provisionally happy with that for now. Here's the second question: Once we've constructed this, we can ask under what conditions the sets Decat(colim(F)) and colim(Decat(F)) are naturally bijective. (I guess there's a natural map from colim(Decat) to Decat(colim).) It's true for filtered index sets; is it true for general index categories? Also, we can generalize these questions to the setting of F be a functor from I to nCat, by which I mean the weak (n+1)-category of all n-categories; then we have a functor of n-categories that we want to represent. Since the notion of "weak n-category" is a matter of some debate, I'm willing to take it for granted that such a colimit does exist. Then: In what context (e.g. for what index categories) do we expect the (n-1)-categories Decat(colim(F)) and colim(Decat(F)) to be equivalent? Or the sets Decat^n(colim(F)) and colim(Decat^n(F))? Again, a definitive answer to that last question is unlikely since it would depend on having a firm grasp of weak n-categories (and of nCat), but I'm curious what people's instincts are. For what it's worth, I can show that Decat can't be a left adjoint (in the relevant sense). If it were, its right adjoint would be a functor F from Set (a 1-category trivially extended to a 2-category) to 1Cat such that, for all categories C and sets S, the category Hom_1Cat(C, FS) is equivalent to the set Hom_Set(Decat(C),S) (thought of as a discrete category). In fact, we can't even have Hom_Set(Decat(C),S) equal Decat(Hom_1Cat(C, FS)). One way to see this is to first let C be the discrete category with two objects, which shows that the cardinality of Decat(FS) is just the cardinality of S. So we might as well assume that the objects of FS are just S and that no two objects are isomorphic. But then set C to be the category 0 -> 1; use this to select a morphism f:s->t for any s,t in S, and then to show that the composite of f:s->t and g:s->t is an isomorphism, so all objects are isomorphic after all. David Carlton carlton@math.stanford.edu 31-Jan-2002 23:01:36 -0400,969;000000000001-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 31 Jan 2002 23:01:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16WTo4-0001Vc-00 for categories-list@mta.ca; Thu, 31 Jan 2002 22:52:04 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 31 Jan 2002 21:30:34 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Diagxy Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk I just uploaded a new version of diagxy.zip to ftp.math.mcgill.ca/pub/barr. The only change is in the documentation and the only change to that is the addition of a page of "thumbnails" of the supplied shapes and their names. 31-Jan-2002 23:01:39 -0400,1865;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 31 Jan 2002 23:01:39 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16WTpM-0002NC-00 for categories-list@mta.ca; Thu, 31 Jan 2002 22:53:24 -0400 User-Agent: Microsoft-Outlook-Express-Macintosh-Edition/5.02.2022 Date: Thu, 31 Jan 2002 14:45:35 +1100 Subject: categories: Re: colimits of categories From: Michael Batanin To: Message-ID: In-Reply-To: <15448.18734.320960.116427@jackfruit.Stanford.EDU> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk on 31/1/02 6:27 AM, david carlton at carlton@math.stanford.edu wrote: > For what it's worth, I can show that Decat can't be a left adjoint (in > the relevant sense). If it were, its right adjoint would be a functor > F from Set (a 1-category trivially extended to a 2-category) to 1Cat > such that, for all categories C and sets S, the category Hom_1Cat(C, > FS) is equivalent to the set Hom_Set(Decat(C),S) (thought of as a > discrete category). > Sorry, when I wrote about Decat as a left adjoint I thought about n-groupoids rather than n-categories. Steve Lack has already clarified the situation. But now I understand you are asking about weak (or pseudo) colimits. They exist in 1-Cat and 2-Cat and can be expressed in terms of appropriate weighted colimits. I never saw a paper about pseudocolimits in 3-Cat (here we can use Gray-categories instead of general tricatgories). They must be expressed as weighted colimits as well, or a codescent object of a simplicial Gray-category. I'd like to have a reference if such a paper already exists. Michael Batanin. 2-Feb-2002 21:35:10 -0400,1644;000000000000-00000000 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 02 Feb 2002 21:35:10 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16XBPT-0006Rq-00 for categories-list@mta.ca; Sat, 02 Feb 2002 21:25:35 -0400 From: Steve Lack MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15450.2840.201243.964061@milan.maths.usyd.edu.au> Date: Fri, 1 Feb 2002 14:27:20 +1100 To: categories@mta.ca Subject: categories: limits in Gray-categories X-Mailer: VM 6.90 under 21.1 (patch 7) "Biscayne" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Michael Batanin writes (in response to David Carlton): > > But now I understand you are asking about weak (or pseudo) colimits. They > exist in 1-Cat and 2-Cat and can be expressed in terms of appropriate > weighted colimits. I never saw a paper about pseudocolimits in 3-Cat (here > we can use Gray-categories instead of general tricatgories). They must be > expressed as weighted colimits as well, or a codescent object of a > simplicial Gray-category. I'd like to have a reference if such a paper > already exists. Some specific examples of weighted limits in the context of Gray-categories are considered in: Stephen Lack, A coherent approach to pseudomonads, Adv. Math. 152:179-202, 2000. In particular, I show that the (suitably pseudo) Eilenberg-Moore object of a pseudomonad can be computed as a weighted limit. But I don't develop the general theory of pseudocolimits in 3-Cat. Steve Lack.