From MAILER-DAEMON Mon Mar 18 04:19:35 2002 Date: Mon, 18 Mar 2002 04:19:35 -0400 (AST) From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE -- FOLDER INTERNAL DATA X-IMAP: 1007392647 0000000052 Status: RO This text is part of the internal format of your mail folder, and is not a real message. It is created automatically by the mail system software. If deleted, important folder data will be lost, and it will be re-created with the data reset to initial values. From rrosebru@mta.ca Mon Dec 3 11:05:19 2001 -0400 >From cat-dist@mta.ca Mon Dec 03 11:05:19 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Dec 2001 11:05:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16AuOz-0000hm-00 for categories-list@mta.ca; Mon, 03 Dec 2001 10:49:01 -0400 X-Received: from zent.mta.ca ([138.73.101.4]) by mailserv.mta.ca with smtp (Exim 3.33 #2) id 16AeVQ-0005X9-00 for rrosebru@mta.ca; Sun, 02 Dec 2001 17:50:36 -0400 X-Received: FROM siv.maths.usyd.edu.au BY zent.mta.ca ; Sun Dec 02 17:49:13 2001 -0400 X-Received: from milan.maths.usyd.edu.au (stevel(.pmstaff;2406.2002)@milan.maths.usyd.edu.au) [129.78.69.163] by siv.maths.usyd.edu.au via smtpdoor V13.2 id 269103 for rrosebru@mta.ca; Mon, 3 Dec 2001 08:49:55 +1100 From: Steve Lack MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15370.41475.333741.89346@milan.maths.usyd.edu.au> Date: Mon, 3 Dec 2001 08:49:55 +1100 To: categories@mta.ca Subject: categories: Re: the walking adjunction and biadjunction X-Mailer: VM 6.90 under 21.1 (patch 7) "Biscayne" XEmacs Lucid Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 James Dolan writes: > are you sure everyone will be happy with the name "biadjunction" for the > thing that you're talking about? i'm just vaguely wondering whether it > might unintentionally evoke ideas about "bicategories". Oops! I guess I fell into this trap. If biadjunction doesn't mean bicategorical adjunction what does it mean? (I mentioned the free-living pseudoadjunction since I thought it did.) Steve. From rrosebru@mta.ca Mon Dec 3 11:05:22 2001 -0400 >From cat-dist@mta.ca Mon Dec 03 11:05:22 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Dec 2001 11:05:22 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16AuWW-0000sE-00 for categories-list@mta.ca; Mon, 03 Dec 2001 10:56:48 -0400 Message-Id: <5.1.0.14.1.20011130181434.009ef8d0@mailx.u-picardie.fr> X-Sender: ehres@mailx.u-picardie.fr X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Sat, 01 Dec 2001 19:20:09 +0100 To: categories@mta.ca From: Andree Ehresmann Subject: categories: Re: the walking adjunction and biadjunction Mime-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 2 On the "walking adjunction" I don't know the Pumplun's paper cited by Wyler. But there is another reference at about the same time; indeed, the "walking adjunction" has been explicitly constructed and studied in the paper of Auderset: "Adjonction et monade au niveau des 2-cat=E9gories" published in "Cahiers de Top. et Geom. Diff." XV-1 (1974), 3-20. More formally it could also be called "the 2-sketch of an adjunction" in the terminology in my paper with Charles Ehresmann: "Categories of sketched structures", in the "Cahiers" XIII-2 (1972), reprinted in "Charles Ehresmann: Oeuvres completes et commentees" Part IV-2. To add a remark on the terminology: When Charles introduced the concept of a sketch (already in a Kansas report of1966, cf. "Oeuvres" Parts III-2 and IV-1), the aim was to define the 'Platonist idea' of a structure, not only of a purely algebraic one, but also of structures like categories (partially defined operations), fields, or even topologies. He thought first of calling a sketch an idea, but then reserved the word "idea" for the smallest part which helps reconstruct the sketch; for instance for a category, the arrows which 'represent' the domain and codomain maps and the composition law. Sincerely Andree C. Ehresmann From rrosebru@mta.ca Mon Dec 3 11:25:45 2001 -0400 >From Andree.Ehresmann@u-picardie.fr Mon Dec 03 11:25:45 2001 Return-path: Envelope-to: CAT-DIST@mta.ca Delivery-date: Mon, 03 Dec 2001 11:25:45 -0400 Received: from zent.mta.ca ([138.73.101.4]) by mailserv.mta.ca with smtp (Exim 3.33 #2) id 16AuyV-00050R-00 for CAT-DIST@mta.ca; Mon, 03 Dec 2001 11:25:43 -0400 Received: FROM siufuxsun04.unifr.ch BY zent.mta.ca ; Mon Dec 03 11:24:22 2001 -0400 Received: from localhost ([127.0.0.1] helo=siufuxsun04.unifr.ch) by siufuxsun04.unifr.ch with esmtp (Exim 3.22 #3) id 16AuyP-0007eD-00 for CAT-DIST@mta.ca; Mon, 03 Dec 2001 16:25:37 +0100 Received: from ufper8.unifr.ch ([134.21.14.68]) by siufuxsun04.unifr.ch with smtp (Exim 3.22 #4) id 16AuyO-0007eB-00 for CAT-DIST@MTA.CA; Mon, 03 Dec 2001 16:25:36 +0100 Received: by ufper6.unifr.ch (MX V4.2 AXP) id 5; Mon, 03 Dec 2001 16:25:35 MET Date: Mon, 03 Dec 2001 16:25:35 MET From: "Andree Ehresmann" To: categories@mta.ca Message-ID: <00A05F9F.998C5769.5@ufper6.unifr.ch> Subject: categories: Re: the walking adjunction and biadjunction Status: O X-Status: X-Keywords: X-UID: 3 Received: from siufuxsun04.unifr.ch by UFPER6.UNIFR.CH via Pony Express SMTP with TCP (v8.1.1-dmr001); Mon, 3 Dec 1 16:25:33 MET Received: from localhost ([127.0.0.1] helo=siufuxsun03.unifr.ch) by siufuxsun04.unifr.ch with esmtp (Exim 3.22 #3) id 16AuyK-0007dt-00 for heinrich.kleisli@unifr.ch; Mon, 03 Dec 2001 16:25:32 +0100 Received: from mailserv.mta.ca ([138.73.101.5]) by siufuxsun03.unifr.ch with esmtp (Exim 3.22 #2) id 16AuyH-0004cM-00 for Heinrich.Kleisli@unifr.ch; Mon, 03 Dec 2001 16:25:29 +0100 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16AuWW-0000sE-00 for categories-list@mta.ca; Mon, 03 Dec 2001 10:56:48 -0400 Message-Id: <5.1.0.14.1.20011130181434.009ef8d0@mailx.u-picardie.fr> X-Sender: ehres@mailx.u-picardie.fr X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Sat, 01 Dec 2001 19:20:09 +0100 To: categories@mta.ca From: Andree Ehresmann Subject: categories: Re: the walking adjunction and biadjunction Mime-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk On the "walking adjunction" I don't know the Pumplun's paper cited by Wyler. But there is another reference at about the same time; indeed, the "walking adjunction" has been explicitly constructed and studied in the paper of Auderset: "Adjonction et monade au niveau des 2-cat=E9gories" published in "Cahiers de Top. et Geom. Diff." XV-1 (1974), 3-20. More formally it could also be called "the 2-sketch of an adjunction" in the terminology in my paper with Charles Ehresmann: "Categories of sketched structures", in the "Cahiers" XIII-2 (1972), reprinted in "Charles Ehresmann: Oeuvres completes et commentees" Part IV-2. To add a remark on the terminology: When Charles introduced the concept of a sketch (already in a Kansas report of1966, cf. "Oeuvres" Parts III-2 and IV-1), the aim was to define the 'Platonist idea' of a structure, not only of a purely algebraic one, but also of structures like categories (partially defined operations), fields, or even topologies. He thought first of calling a sketch an idea, but then reserved the word "idea" for the smallest part which helps reconstruct the sketch; for instance for a category, the arrows which 'represent' the domain and codomain maps and the composition law. Sincerely Andree C. Ehresmann From rrosebru@mta.ca Mon Dec 3 20:35:59 2001 -0400 >From cat-dist@mta.ca Mon Dec 03 20:35:59 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Dec 2001 20:35:59 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16B3V6-0006yo-00 for categories-list@mta.ca; Mon, 03 Dec 2001 20:31:56 -0400 Date: Mon, 3 Dec 2001 13:23:40 -0500 (EST) From: F W Lawvere Reply-To: wlawvere@acsu.buffalo.edu To: categories@mta.ca Subject: categories: representing adjunctions Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 4 ONE MORE HISTORICAL CITATION The Pumplun paper cited by Wyler as well as the Auderset paper cited by Mme Ehresmann illustrate that the study of generic structures in 2-categories has been going on for some time. My own paper ORDINAL SUMS AND EQUATIONAL DOCTRINES, SLNM 80 (1969) 141-155 shows that the augmented simplicial category Delta serves as the generic monad, but moreover goes on to actually apply this to show that the Kleisli construction is a tensor product left-adjoint to the Eilenberg- Moore construction which is an enriched Hom. The Hom/tensor formalism appropriate to the case of strict monoid objects is all that is required here, as I will explain below. AN EXTENSION AND A RESTRICTION The important special case of FROBENIUS monads is explicitly characterized in three ways in my paper. Concerning the IDEMPOTENT case discussed a few days ago by Grandis and Johnstone, note that the publication of Schanuel and Street proves among other things that the monoid Delta in Cat has very few quotients (see below for significance of the monoid structure). THE GENERAL HOM/TENSOR FORMALISM AND A VERY PARTICULAR MONOID In any cartesian-closed category with finite limits and co-limits, a non-linear version of the Cartan-Eilenberg Hom/tensor formalism applies to actions and biactions of monoid objects. In Cat, Delta is a (strict) monoid and its actions are precisely monads on arbitrary categories. A crucial part of the formalism is that categories of actions are automatically enriched in the basic cartesian-closed category, which in this case is Cat. There is a particular biaction of Delta, which I called Delta plus, with the property that the enriched Hom of it into an arbitrary Delta-action is exactly the Eilenberg-Moore category of "algebras", automatically equipped with its structure as a Delta^op action (co-monad). The left-adjoint tensor assigns to any category equipped with a co-monad its Kleisli category, as a category with monad. Not only are the calculations in this particular case quite explicit, but the enriched Hom tensor formalism has a lot of content which is still under-exploited. SKETCHES VERSUS PLATONISM The often repeated slander that mathematicians think "as if" they were "platonists" needs to be combatted rather than swallowed. What mathematicians and other scientists use is the objectively developed human instrument of general concepts. (The plan to misleadingly use that fact as a support for philosophical idealism may have been an honest mistake by Plato, or it may have been part of his job as disinformation officer for the Athenian CIA organization; it probably would not have survived until now had it not been for the special efforts of Cosimo de' Medici.) It seems that a general concept has two related aspects, as I began to realize more explicitly in connection with my paper Adjointness in foundations, Dialectica vol. 23, 1969 281-296; I later learned that some philosophers refer to these two aspects as "abstract general vs. concrete general". For example, there is the algebraic theory of rings vs. the category of all rings, or a particular abstract group vs. the category of all permutation representations of the group. While it is "obvious" that, at least in mathematics, a concrete general should have the structure of a category, because all the instances embody the same abstract general and hence any two instances can be compared in preferred ways, by contrast it was not until the late fifties that one realized that an abstract general can also be construed as a category in its own right. That realization essentially made explicit the fact that substitution is a logical operation and indeed is the most fundamental logical operation. Thus an abstract general is essentially a special algebraic structure indeed a category with additional structure such as finite limits or still richer doctrines. As with other algebraic structures there are again two aspects, the structures themselves and their presentations which are closely related, yet quite distinct; for example, more than one presentation may be needed for efficient calculations determining features of the same algebraic structure. What is meant by a presentation depends on the doctrine: for example Delta as a mere category has an infinite presentation used in topology, but as a strict monoidal category it has a finite presentation. The notion of SKETCH is the most efficient scheme yet devised for the general construction of PRESENTATIONS OF ABSTRACT GENERALS. The fact that particular abstract generals and the idea of sketches exist within the historically developed objective science does not mean that they somehow always existed; to call them "platonic" seems to detract from the honor of their actual discoverers. Bill Lawvere ************************************************************ 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 ************************************************************ From rrosebru@mta.ca Mon Dec 3 20:37:10 2001 -0400 >From cat-dist@mta.ca Mon Dec 03 20:37:10 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Dec 2001 20:37:10 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16B3a4-0006Vk-00 for categories-list@mta.ca; Mon, 03 Dec 2001 20:37:04 -0400 Date: Mon, 3 Dec 2001 12:49:52 -0800 From: Toby Bartels To: categories@mta.ca Subject: categories: Re: the walking adjunction and biadjunction Message-ID: <20011203124952.A1223@math-cl-n03.ucr.edu> References: <5.1.0.14.1.20011130181434.009ef8d0@mailx.u-picardie.fr> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i In-Reply-To: <5.1.0.14.1.20011130181434.009ef8d0@mailx.u-picardie.fr>; from Andree.Ehresmann@u-picardie.fr on Sat, Dec 01, 2001 at 07:20:09PM +0100 Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 5 Andree Ehresmann wrote in part: >He thought >first of calling a sketch an idea, but then reserved the word "idea" for >the smallest part which helps reconstruct the sketch; for instance for a >category, the arrows which 'represent' the domain and codomain maps and the >composition law. There could be multiple ideas that generate the same sketch; how do we decide which is the correct idea among equivalent ones? OTOH, if we take equivalence classes of ideas, then we're taking sketches. For example, one could define the idea of multiplication in a monoid as a binary operation and a nullary operation or alternatively as an operation on finite tuples. The former is more common, but I prefer the latter; who has the right idea? -- Toby toby@math.ucr.edu From rrosebru@mta.ca Mon Dec 3 20:40:19 2001 -0400 >From cat-dist@mta.ca Mon Dec 03 20:40:19 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Dec 2001 20:40:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16B3cy-0004FI-00 for categories-list@mta.ca; Mon, 03 Dec 2001 20:40:04 -0400 Date: Mon, 3 Dec 2001 08:50:01 -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 Status: O X-Status: X-Keywords: X-UID: 6 Dear Colleagues: We are pleased to announce that a "Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories" will be held September 23-28, 2002, at the Fields Institute in Toronto. For a general description of the theme of the Workshop, see below. A second and more detailed announcement will be sent in January 2002. It will contain a list of invited talks as well as an invitation for a limited number of contributed talks. There is also a webpage about the Workshop at http://www.fields.utoronto.ca/programs/scientific/02-03/galois_and_hopf/ We hope to be able to welcome you at the Workshop. George Janelidze (george_janelidze@hotmail.com) Bodo Pareigis (pareigis@rz.mathematik.uni-muenchen.de) Walter Tholen (tholen@mathstat.yorku.ca) > Theme and Purpose of the Workshop > > The goal of the meeting is to spread and to advance categorical > methods and their application amongst researchers working in three > overlapping areas of algebra, namely in the study of > > (I) algebraic structures in monoidal categories and their classical > examples, such as Hopf, Frobenius, and Azumaya algebras, and others, > particularly those occurring in quantum field theory, > > (II) Galois theory vis-a-vis Grothendieck's descent theory, as well as the > general theory of separability and decidability, applied particularly to the > structures mentioned in (I), > > (III) homological algebra of non-abelian structures, such as groups, rings > and (associative or Lie) algebras, and its extension to the structures > mentioned in (I). > > The categorical methods used will include > > (i) 2- and higher-dimensional categorical structures, especially > symmetric/braided monoidal categories, > > (ii) categorical Galois theory, monads and fibrational descent theory, and > > (iii) the recently developed theory of protomodular and, more specifically, > semiabelian categories, which provides a convenient categorical setting to > pursue classical group-theroretic and homological concepts in a very general > context. From rrosebru@mta.ca Mon Dec 3 20:54:58 2001 -0400 >From cat-dist@mta.ca Mon Dec 03 20:54:58 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 03 Dec 2001 20:54:58 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16B3qk-0008BE-00 for categories-list@mta.ca; Mon, 03 Dec 2001 20:54:18 -0400 From: Malvina Nissim Date: Fri, 30 Nov 2001 18:39:31 GMT Message-Id: <200111301839.SAA11756@banks.cogsci.ed.ac.uk> To: categories@mta.ca Subject: categories: ESSLLI 2002 Student Session Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 7 !!! Concerns all students in Logic, Linguistics and Computer Science !!! !!! Please circulate and post among students !!! We apologise if you receive this message more than once. ESSLLI-2002 STUDENT SESSION FIRST CALL FOR PAPERS August 5-16 2002, Trento, Italy Deadline: February 25th, 2002 www.iccs.informatics.ed.ac.uk/~malvi/esslli02 We are pleased to announce the Student Session of the 14th European Summer School in Logic, Language and Information (ESSLLI-2002) organised by the Centre for scientific and technological research (ITC-irst) in Trento and by the University of Trento, under the auspices of the European Association for Logic, Language and Information (FoLLI). ESSLLI-2002 will be held in Trento from August 5-16 2002. We invite submission of papers for presentation at the ESSLLI-2002 Student Session and for appearance in the proceedings. PURPOSE: This seventh ESSLLI Student Session will provide, like the other editions, an opportunity for ESSLLI participants who are students to present their own work in progress and get feedback from senior researchers and fellow-students. The ESSLLI Student Session encourages submissions from students at any level, from undergraduates (before completion of the Master Thesis) as well as postgraduates (before completion of the PhD degree). Papers co-authored by non-students will not be accepted. Papers may be accepted for full presentation (30 minutes including 10 minutes of discussion) or for a poster presentation. All the accepted papers will be published in the ESSLLI-2002 Student Session proceedings, which will be made available during the summer school. KLUWER BEST PAPER AWARD: As in previous years, the best paper will be selected by the programme committee and will be offered a prize by Kluwer Academic Publishers to be spent on books. REQUIREMENTS: The Student Session papers should describe original, unpublished work, completed or in progress that demonstrates insight, creativity, and promise. No previously published papers should be submitted. Note that the ESSLLI02 school will be focussed on the three main interdisciplinary areas (Logic & Language, Logic & Computation, and Language & Computation), while the single areas have been dropped. Given the high interest shown over the years, the Student Session will keep two of the single areas, namely Logic and Language, welcoming thus submissions within the following topics: Logic, Language, Logic & Language, Logic & Computation, Language & Computation. FORMAT OF SUBMISSION: Student authors should submit an anonymous full paper headed by the paper title, not to exceed 7 pages of length exclusive of references and send a separate identification page (see below). Note that the length of the final version of the accepted papers will not be allowed to exceed 10 pages. Since reviewing will be blind, the body of the abstract should omit author names and addresses. Furthermore, self-references that reveal the author's identity (e.g., "We previously showed (Smith, 1991)... ") should be avoided. It is possible to use instead references like "Smith (1991) previously showed...". For any submission, a plain ASCII text version of the identification page should be sent separately, using the following format: Title: title of the submission First author: firstname lastname Address: address of the first author ...... Last author: firstname lastname Address: address of the last author Short summary: abstract (5 lines) Subject area (one of): Logic | Language | Logic and Language | Logic and Computation | Language and Computation If necessary, the program committee may reassign papers to a more appropriate subject area. The submission of the extended abstract should be in one of the following formats: PostScript, PDF, RTF, or plain text. But note that, in case of acceptance, the final version of the paper has to be submitted in LaTeX format. Please, use A4 size pages, 11pt or 12pt fonts, and standard margins. Submissions outside the specified length and formatting requirements may be subject to rejection without review. The paper and separate identification page must be sent by e-mail to: malvi@cogsci.ed.ac.uk by FEBRUARY 25th 2002 ESSLLI-2002 INFORMATION: In order to present a paper at ESSLLI-2002 Student Session, at least one student author of each accepted paper has to register as a participant at ESSLLI-2002. The authors of accepted papers will be eligible for reduced registration fees. For all information concerning ESSLLI-2002, please consult the ESSLLI-2002 web site at www.esslli2002.it IMPORTANT DATES: Deadline for submission of abstracts: February 25, 2002. Authors Notifications: April 22, 2002. Final version due: May 20, 2002. ESSLLI-2002 Student Session: August 5-16, 2002. PROGRAMME COMMITTEE: David Ahn, University of Rochester (Language and Computation) Carlos Areces, University of Amsterdam (Logic) Reinhard Blutner, University of Berlin (Language) Kees van Deemter, University of Brighton (Language and Computation) Paul Dekker, University of Amsterdam (Logic and Language) Juergen Dix, University of Manchester (Logic and Computation) Marta Garcia-Matos, University of Helsinki (Logic) Juan Heguiabehere, University of Amsterdam (Logic and Computation) Elsi Kaiser, University of Pennsylvania (Language) Malvina Nissim, University of Edinburgh (Chair) Rick Nouwen, University of Utrecht (Logic and Language) For any specific question concerning ESSLLI-2002 Student Session, please, do not hesitate to contact me: Malvina Nissim ICCS, University of Edinburgh 2 Buccleuch Place, Edinburgh EH8 9LW, UK phone: +44 +(0)131 +650 4630 fax: +44 +(0)131 +650 6626 e-mail: malvi@cogsci.ed.ac.uk From rrosebru@mta.ca Tue Dec 4 20:38:20 2001 -0400 >From cat-dist@mta.ca Tue Dec 04 20:38:20 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 Dec 2001 20:38:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16BPuH-000819-00 for categories-list@mta.ca; Tue, 04 Dec 2001 20:27:25 -0400 From: baez@math.ucr.edu Message-Id: <200112040342.fB43gfM10526@math-cl-n05.ucr.edu> Subject: categories: Sketches and Platonic Ideas To: categories@mta.ca (categories) Date: Mon, 3 Dec 2001 19:42:40 -0800 (PST) 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 Status: O X-Status: X-Keywords: X-UID: 8 Toby Bartels writes: > There could be multiple ideas that generate the same sketch; > how do we decide which is the correct idea among equivalent ones? > OTOH, if we take equivalence classes of ideas, then we're taking sketches. > For example, one could define the idea of multiplication in a monoid > as a binary operation and a nullary operation > or alternatively as an operation on finite tuples. > The former is more common, but I prefer the latter; > who has the right idea? I'm confused: in my understanding, a sketch basically amounts to a way of giving generators and relations for a category with products, Different sketches give the same category with products, not vice versa. Your example gives two sketches, but one category with products. In this sense, a sketch is more like an "idea" than you seem to be giving it credit for. By the way, in response to Lawvere's comments: My use of the term "Platonic idea of X" for the free category/category with products/monoidal category/2-category/whatever on an X was not meant as an endorsement of "Platonism" in the philosophy of mathematics - especially since "Platonism" means many things to many people. It was also not meant to suggest that Plato had this idea. It was basically meant to get people thinking about abstract generals versus concrete particulars. Best, John Baez From rrosebru@mta.ca Wed Dec 5 15:25:52 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 05 Dec 2001 15:25:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16BhWu-0005mB-00 for categories-list@mta.ca; Wed, 05 Dec 2001 15:16:28 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Wed, 5 Dec 2001 08:59:11 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories Subject: categories: Re: Sketches and Platonic Ideas In-Reply-To: <200112040342.fB43gfM10526@math-cl-n05.ucr.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 9 There are a number of definitions of sketch around, some of which require it to be a category with finite products. In one of Ehresmann's (and Bastiani's, I believe) there is mentioned the possibility of its being what they called a quasicategory (or some such substructure term) in which composition is a partly defined multi-ary operation (in other words, fgh could be defined without fg or gh being defined). Charles and I realized that this was equivalent to what we called a graph with diagrams, which seemed a more useable notion. So what we called a sketch was a graph with diagrams as well as certain cones and cocones that were singled out to be taken to limits and colimits, resp. Peter Johnstone criticized us for doing the equivalent of replacing groups by generators and relations, which is correct, but it was a conscious decision and there were reasons for it. I had never heard the term "idea" in this connection or we might have used it. But anyway, "sketch" is used in different ways and I guess Charles and I contributed to this, but didn't create it. On Mon, 3 Dec 2001 baez@math.ucr.edu wrote: > Toby Bartels writes: > > > There could be multiple ideas that generate the same sketch; > > how do we decide which is the correct idea among equivalent ones? > > OTOH, if we take equivalence classes of ideas, then we're taking sketches. > > For example, one could define the idea of multiplication in a monoid > > as a binary operation and a nullary operation > > or alternatively as an operation on finite tuples. > > The former is more common, but I prefer the latter; > > who has the right idea? > > I'm confused: in my understanding, a sketch basically amounts to > a way of giving generators and relations for a category with products, > Different sketches give the same category with products, not vice versa. > Your example gives two sketches, but one category with products. In > this sense, a sketch is more like an "idea" than you seem to be giving > it credit for. > > By the way, in response to Lawvere's comments: > > My use of the term "Platonic idea of X" for the free > category/category with products/monoidal category/2-category/whatever > on an X was not meant as an endorsement of "Platonism" in the philosophy > of mathematics - especially since "Platonism" means many things to > many people. It was also not meant to suggest that Plato had this idea. > It was basically meant to get people thinking about abstract generals > versus concrete particulars. > > Best, > John Baez > > > > > > From rrosebru@mta.ca Wed Dec 5 15:25:53 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 05 Dec 2001 15:25:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16BheI-0006NV-00 for categories-list@mta.ca; Wed, 05 Dec 2001 15:24:07 -0400 Subject: categories: Re: the walking adjunction and biadjunction To: categories@mta.ca Date: Tue, 4 Dec 2001 02:29:56 +0000 (GMT) X-Mailer: ELM [version 2.5 PL5] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: From: Tom Leinster X-Scanner: exiscan *16B5LI-0001Sg-00*0QLuVhmB0e2* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 10 Toby Bartels wrote: > > For example, one could define the idea of multiplication in a monoid > as a binary operation and a nullary operation > or alternatively as an operation on finite tuples. > The former is more common, but I prefer the latter; > who has the right idea? An interesting question in itself. I don't think either idea is "right", but I (presumably) share with you the feeling that often the latter is more appropriate. However, if you resolve wholeheartedly never to use a binary + nullary presentation of a monoid-like structure then you actually find yourself in quite an extreme position. For instance, a monoid would be defined as a set M together with an n-fold operation (m_1, ..., m_n) |---> [m_1 ... m_n] on M for each natural n, subject to axioms. This is as expected so far, but we've disallowed ourselves from using what would probably be the natural choice of axioms, [[m_1^1 ... m_1^{k_1}] ... [m_n^1 ... m_n^{k_n}]] = [m_1^1 ... m_n^{k_n}], m = [m], since this is a binary + nullary presentation. So instead we should derive from the n-fold multiplications a k-ary operation o_T on M for each (finite, planar) k-leafed tree T; and the axioms then become that o_T = o_U for any two k-leafed trees T and U. The situation gets more extreme still if you want a wholeheartedly non-binary-and-nullary presentation of the notion of monoidal category. We have an underlying category M, an n-fold tensor functor for each n, and then coherence cells obeying coherence axioms. The obvious choice for the coherence cells comes from turning the two equations above into specified isomorphisms, but again this is disallowed, so we have to specify a coherence cell o_T --~--> o_U for each T and U, where o_T, o_U are now derived tensor functors. Then we need to put axioms on the coherence cells, and once more the obvious way of doing this involves something of a binary + nullary character. Specifically, you have to make sure that the coherence cells o_T --~--> o_U are compatible with "grafting of trees", which means taking a k-leafed tree T and sticking onto its leaves k trees T_1, ..., T_k, to make a new tree T(T_1, ..., T_k) - but this expression has *2* (bad number!) levels of trees. So we need to replace these axioms with equivalent non-binary-and-nullary ones, and this means considering more complicated structures still. (The considerations in the last paragraph are really to do with writing down a non-binary-and-nullary presentation of the theory of operads, which are themselves monoids of a sort.) Tom From rrosebru@mta.ca Wed Dec 5 16:16:53 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 05 Dec 2001 16:16:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16BiSe-0002VD-00 for categories-list@mta.ca; Wed, 05 Dec 2001 16:16:08 -0400 X-Originating-IP: [128.205.249.50] From: "F. William Lawvere" To: categories@mta.ca Subject: categories: Re: Sketches and Platonic Ideas Date: Wed, 05 Dec 2001 04:36:21 Mime-Version: 1.0 Content-Type: text Message-ID: Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 11 Certainly I did not mean to suggest that either John or Andree were supporting platonism as a philosophy of mathematics. In fact I had momentarily even forgotten that John had used the term. In my 1972 Perugia Notes I had made an attempt to characterize the relation between these sorts of mathematical considerations and philosophy by saying that while platonism is wrong on the relation between Thinking and Being, something analogous is correct WITHIN the realm of Thinking. The relevant dialectic there is between abstract general and concrete general. Not concrete particular ("concrete" here does not mean "real").There is another crucial dialectic making particulars (neither abstract nor concrete) give rise to an abstract general; since experiments do not mechanically give rise to theory, it is harder to give a purely mathematical outline of how that dialectic works, though it certainly does work. A mathematical model of it can be based on the hypothesis that a given set of particulars is somehow itself a category (or graph), i.e., that the appropriate ways of comparing the particulars are given but that their essence is not. Then their "natural structure" (analogous to cohomology operations) is an abstract general and the corresponding concrete general receives a Fourier-Gelfand-Dirac functor from the original particulars. That functor is usually not full because the real particulars are infinitely deep and the natural structure is computed with respect to some limited doctrine; the doctrine can be varied, or "screwed up or down" as James Clerk Maxwell put it, in order to see various phenomena. From: baez@math.ucr.edu >To: categories@mta.ca (categories) >Subject: categories: Sketches and Platonic Ideas >Date: Mon, 3 Dec 2001 19:42:40 -0800 (PST) > >Toby Bartels writes: > >> There could be multiple ideas that generate the same sketch; >> how do we decide which is the correct idea among equivalent ones? >> OTOH, if we take equivalence classes of ideas, then we're taking sketches. ... >> who has the right idea? > > I'm confused: in my understanding, a sketch basically amounts to ... >By the way, in response to Lawvere's comments: > > My use of the term "Platonic idea of X" for the free ... >versus concrete particulars. >Best, >John Baez From rrosebru@mta.ca Thu Dec 6 09:10:59 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Dec 2001 09:10:59 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16ByCV-0006AV-00 for categories-list@mta.ca; Thu, 06 Dec 2001 09:04:31 -0400 Message-Id: <5.1.0.14.2.20011205155136.02024090@mail.oberlin.net> X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Wed, 05 Dec 2001 15:52:29 -0500 To: categories@mta.ca From: Charles Wells Subject: categories: Sketches Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 12 This is in reply to Toby Bartels, quoted below. I don't believe that those of us who have written about "ideas" in Ehresmann's sense ever conceived that each theory (sketch) was based on one right idea. There is no "correct" idea for a given sketch. I want to add, for those new to the subject, that the word "sketch" has been used with at least three meanings. Ehresmann and his students use it for a structure which is a weakening of the concept of category (the composite may not be defined for all composable pairs) plus specified cones and/or cocones. Many others have used the word sketch to refer to a category with specified cones and/or cocones. Michael Barr and I in our two books used "sketch" to mean a graph with specified cones and/or cocones plus some commutativity conditions on paths; that is in the same spirit as Ehresmann's "idea". --Charles Wells >Andree Ehresmann wrote in part: > > >He thought > >first of calling a sketch an idea, but then reserved the word "idea" for > >the smallest part which helps reconstruct the sketch; for instance for a > >category, the arrows which 'represent' the domain and codomain maps and the > >composition law. > >There could be multiple ideas that generate the same sketch; >how do we decide which is the correct idea among equivalent ones? >OTOH, if we take equivalence classes of ideas, then we're taking sketches. >For example, one could define the idea of multiplication in a monoid >as a binary operation and a nullary operation >or alternatively as an operation on finite tuples. >The former is more common, but I prefer the latter; >who has the right idea? > > >-- Toby > toby@math.ucr.edu 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 From rrosebru@mta.ca Thu Dec 6 09:11:02 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Dec 2001 09:11:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16ByEU-0005PA-00 for categories-list@mta.ca; Thu, 06 Dec 2001 09:06:34 -0400 Date: Thu, 6 Dec 2001 00:23:14 -0800 From: Toby Bartels To: categories@mta.ca Subject: categories: Sketches and ideas (Was: the walking adjunction and biadjunction) Message-ID: <20011206002314.A401@math-cl-n03.ucr.edu> 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 T.Leinster@dpmms.cam.ac.uk on Tue, Dec 04, 2001 at 02:29:56AM +0000 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 13 Tom Leinster wrote in part: >Toby Bartels wrote: >>For example, one could define the idea of multiplication in a monoid >>as a binary operation and a nullary operation >>or alternatively as an operation on finite tuples. >>The former is more common, but I prefer the latter; >>who has the right idea? >An interesting question in itself. I don't think either idea is "right", That was supposed to be my point. Just as a group can be described many ways by generators and relations, so a sketch (if we define a sketch to be an entire category; apparently that varies) can be described many ways by ideas. It's the category that truly characterises what a monoid is (in the given doctrine), so it better deserves the name "idea", if we're trying to hark back to Plato-n (even just to be cute). (Whether or not it's too late to change, I can't say.) >we've disallowed ourselves from using what would probably be the natural >choice of axioms, >[[m_1^1 ... m_1^{k_1}] ... [m_n^1 ... m_n^{k_n}]] = [m_1^1 ... m_n^{k_n}], >m = [m], >since this is a binary + nullary presentation. 2 indices and 0 indices. *Gulp* You're right! I always felt annoyed having to write in that nullary axiom; now I know why. >So instead we should derive >from the n-fold multiplications a k-ary operation o_T on M for each (finite, >planar) k-leafed tree T; and the axioms then become that o_T = o_U for any >two k-leafed trees T and U. I suppose that you're aware of this, but note that we need to allow nodes that don't branch but also aren't labelled (considered leaves), which is where we place []. For example, the tree m . \ / \ / \./ indicates the product [m[]]; that it equals m is the right unit law. This threw me for a moment, since [] seemed at first to have disappeared. We could also go straight to trees and define them as the basic operations, then requiring as axiom that grafting of trees produces the same result as composing the operations. If we were defining a nonassociative operation without identity, then we could denote the basic operations by *binary* trees. >Specifically, you have to make sure that the coherence cells o_T >--~--> o_U are compatible with "grafting of trees", which means taking a >k-leafed tree T and sticking onto its leaves k trees T_1, ..., T_k, to make a >new tree T(T_1, ..., T_k) - but this expression has *2* (bad number!) levels >of trees. The nullary counterpart is grafting 0 trees to get the tree m. >So we need to replace these axioms with equivalent >non-binary-and-nullary ones, and this means considering more complicated >structures still. Well, I managed to introduce grafting back before the categorification! Aren't I clever? Too clever for my own good? ^_^ >(The considerations in the last paragraph are really to do with writing down >a non-binary-and-nullary presentation of the theory of operads, which are >themselves monoids of a sort.) As long as we learn the lesson that binary operations warrant a search for their nullary partners, then we've done the important thing, at least, even if we miss out on some ever more complicated elegance. -- Toby toby@math.ucr.edu From rrosebru@mta.ca Thu Dec 6 17:03:38 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Dec 2001 17:03:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16C5bV-0000wP-00 for categories-list@mta.ca; Thu, 06 Dec 2001 16:58:49 -0400 Date: Thu, 6 Dec 2001 09:00:12 -0500 (EST) From: Oswald Wyler To: Subject: categories: Reference wanted Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 14 I'm sure that the following is known, but I've never seen it in print. Does someone have a reference for it? Proposition. Let U be a monadic functor, in the sense of Mac Lane's CWM. If U factors U=HG with H faithful and amnestic, and G having a left adjoint, then G is monadic. From rrosebru@mta.ca Thu Dec 6 17:03:41 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Dec 2001 17:03:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16C5b7-0002rs-00 for categories-list@mta.ca; Thu, 06 Dec 2001 16:58:25 -0400 Message-Id: <3.0.6.16.20011206082852.4ccf0ab6@pop3.norton.antivirus> X-Sender: cxm7/pop.cwru.edu@pop3.norton.antivirus X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (16) Date: Thu, 06 Dec 2001 08:28:52 To: categories@mta.ca From: Colin McLarty Subject: categories: Two Days Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 Working on the history of category theory I find that Mahlon Marsh Day hired several category theorists at the University of Illinois Champaign-Urbana in the 1960s. I would like to know whatever people can tell me about his connections to category theory--perhaps through Eilenberg? Also, does anyone here know whether Mahlon Michael Day was Mahlon Marsh Day's son? Mahlon Michael Day got a PhD at Chicago in 1967 with Kaplansky. Thanks, Colin From rrosebru@mta.ca Fri Dec 7 20:08:45 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUsQ-0000up-00 for categories-list@mta.ca; Fri, 07 Dec 2001 19:57:58 -0400 Message-Id: <5.1.0.14.2.20011206155739.0204cd50@mail.oberlin.net> X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Thu, 06 Dec 2001 15:58:53 -0500 To: categories@mta.ca From: Charles Wells Subject: categories: Defining monoids Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 In talking about defining monoids, Toby Bartels wrote: "We could also go straight to trees and define them as the basic operations, then requiring as axiom that grafting of trees produces the same result as composing the operations." This is the mu operation of the corresponding monad. Every single-sorted "idea" in the sense of the recent discussion generates a monad in sets with a mu like this. For each set S there is a set of possible computations TS, a mu:TTS to TS, and a "OneIdentity" operation in the sense of Mathematica that says the computation consisting of a single node results in that node; these subject to the monad laws. In other words, the phenomenon you noted is an instance of a general result. --Charles Wells 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 From rrosebru@mta.ca Fri Dec 7 20:08:45 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUy8-0006JA-00 for categories-list@mta.ca; Fri, 07 Dec 2001 20:03:52 -0400 From: Martin Escardo MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Date: Fri, 7 Dec 2001 15:20:07 +0000 (GMT) To: categories@mta.ca Subject: categories: CFP: Workshop Domains VI X-Mailer: VM 6.43 under 20.4 "Emerald" XEmacs Lucid Message-ID: <15376.56699.391842.519063@henry.cs.bham.ac.uk> Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 Call for abstracts Domains VI Birmingham, 16-19 September 2002. The Workshop on Domains is aimed at computer scientists and mathematicians alike who share an interest in the mathematical foundations of computation. The workshop will focus on domains, their applications and related topics. Previous meetings were held in Darmstadt (94,99), Braunschweig (96), Munich (97) and Siegen (98). The emphasis is on the exchange of ideas between participants similar in style to Dagstuhl seminars. INVITED SPEAKERS Ulrich Berger University of Wales Swansea Thierry Coquand Goeteborg University Jimmie Lawson Louisiana State University John Longley University of Edinburgh * Dag Normann University of Oslo Prakash Panangaden McGill University Uday Reddy University of Birmingham Thomas Streicher Darmstadt University * to be confirmed SCOPE Domain theory has had applications to programming language semantics and logics (lambda-calculus, PCF, LCF), recursion theory (Kleene-Kreisel countable functionals), general topology (injective spaces, function spaces, locally compact spaces, Stone duality), topological algebra (compact Hausdorff semilattices) and analysis (measure, integration, dynamical systems). Moreover, these applications are related - for example, Stone duality gives rise to a logic of observable properties of computational processes. As such, domain theory is highly interdisciplinary. Topics of interaction with domain theory for this workshop include, but are not limited to: program semantics program logics probabilistic computation exact computation over the real numbers lambda calculus games models of sequential computation constructive mathematics recursion theory realizability real analysis topology locale theory metric spaces category theory topos theory type theory SUBMISSION OF ABSTRACTS One-page abstracts should be submitted to domainsvi@cs.bham.ac.uk Shortly after an abstract is submitted (usually one or two weeks), the authors will be notified by the programme committee. Abstracts will be dealt with on a first-come/first-served basis. DEADLINE 30 April 2002 ACCOMODATION We meeting will take place at "The Manor House" halls of residence of the University of Birmingham (http://www.bham.ac.uk/conferences/#Manor). More details will be provided at a later date. PROGRAMME COMMITTEE Martin Escardo University of Birmingham Achim Jung University of Birmingham Klaus Keimel Darmstadt University Alex Simpson University of Edinburgh ORGANIZATION COMMITTEE Martin Escardo University of Birmingham Achim Jung University of Birmingham PUBLICATION We plan to publish proceedings of the workshop in lecture notes series. There will be a call for papers after the workshop takes place. The papers will be refereed according to normal publication standards. URL http://www.cs.bham.ac.uk/~wd6/index.html From rrosebru@mta.ca Fri Dec 7 20:08:48 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:48 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUvt-0001Ev-00 for categories-list@mta.ca; Fri, 07 Dec 2001 20:01:33 -0400 Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 7 Dec 2001 11:43:05 +0100 To: categories@mta.ca From: grandis@dima.unige.it (Marco Grandis) Subject: categories: Preprint: Directed homotopy theory, II. Homotopy constructs, Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 18 The following preprint is available: M. Grandis, Directed homotopy theory, II. Homotopy constructs, Dip. Mat. Univ. Genova, Preprint 446 (Dec 2001). (19 p.) ___ Abstract. Directed Algebraic Topology studies phenomena where privileged directions appear, derived from the analysis of concurrency, traffic networks, space-time models, etc. This is the sequel of a paper, 'Directed homotopy theory, I. The fundamental category', where we introduced directed spaces, their non reversible homotopies and their fundamental category. Here we study some basic constructs of homotopy, like homotopy pushouts and pullbacks, mapping cones and homotopy fibres, suspensions and loops, cofibre and fibre sequences. ___ Part I and II are available, in ps: ftp://www.dima.unige.it/Home/grandis/public/Dht1.ps ftp://www.dima.unige.it/Home/grandis/public/Dht2.ps ___ 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/ From rrosebru@mta.ca Fri Dec 7 20:08:48 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:48 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUuW-0001pd-00 for categories-list@mta.ca; Fri, 07 Dec 2001 20:00:08 -0400 Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 7 Dec 2001 12:30:42 +0100 To: categories@mta.ca From: Giovanni Sambin Subject: categories: 2WFTop: information update Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 19 information update about the: SECOND WORKSHOP ON FORMAL TOPOLOGY Auditorium S. Margherita, Campo S. Margherita Venice, April 4-6, 2002 The first announcement can now be found, together with updated information, on the web page http://www.math.unipd.it/~logic/wftop2 Here follow the main variations with respect to the first announcement: Invited speakers. The list of invited speakers now includes Bernhard Banaschewski, Martin Escardo, Henri Lombardi, Christopher Mulvey, Peter Johnstone, Erik Palmgren, Mike Smyth, Steve Vickers. Tutorials. One day, 3 April 2002, of tutorials by Peter Aczel, Bernhard Banaschewski, Giovanni Sambin and Silvio Valentini. Accomodation. Due to the number of requests, we booked two buildings, so that now the safe deadline for booking convenient accomodation is extended to 31 December 2001. Important dates: December 31, 2001 : early registration (with safe accomodation) February 28, 2002: deadline for the submission of papers March 15, 2002: program is decided April 3, 2002: tutorials April 4 - 6, 2002: workshop April 7: trip by private boat on the lagoon Registration and accomodation. The form below must be sent to Damiano Macedonio, mace@dsi.unive.it. Name and Family name: Institution: Address: E-mail address: Date of arrival: Date of departure: Kind of accomodation (if required): low cost (Palazzo Zenobio, room with 3-4 beds, 15-30 euros each person) double rooms (Fondazione Levi or Palazzo Zenobio, with bathroom, 40-60 euros each person) single rooms (a very limited number of them is available) From rrosebru@mta.ca Fri Dec 7 20:08:51 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:51 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUz4-0000wm-00 for categories-list@mta.ca; Fri, 07 Dec 2001 20:04:50 -0400 Message-Id: <3.0.6.16.20011207110923.51571d2e@pop3.norton.antivirus> X-Sender: cxm7/pop.cwru.edu@pop3.norton.antivirus X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (16) Date: Fri, 07 Dec 2001 11:09:23 To: categories@mta.ca From: Colin McLarty Subject: categories: Why exact categories? history Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 20 Myles Tierney has told me about a perspective on exact categories, in the 1960s, that I had not understood. I probably still do not see it very much the way it looked then. So I ask about it here. What were the reasons for studying exact categories in the 1960s? Here is what I used to think: Every additive category with a generator has a faithful functor to the category of Abelian groups. MacLane had explored this idea in 1950. Then Grothendieck's Tohoku paper axiomatized Abelian categories in a more useful way for homological algebra, and showed that all sheaf categories satisfied the axioms (i.e. sheaves of Abelian groups on topological spaces, and the key theorem says they have enough injectives). That created two reasons to look for a non-additive generalization. First, to extend from Abelian groups to all groups, for use in non-Abelian cohomology. (MacLane had already hinted at replacing Abelian groups by all groups in 1950). And second to axiomatize sheaves of sets. The exact category axioms were a promising non-additive analogue to the Abelian category axioms. And I have always thought of the Abelian category embedding theorems as proving that, if you want to, you can think of Abelian categories as concrete categories with the natural limits and colimits. Myles did not disagree with any of that but he put it this way: Not all categories enriched in Abelian groups are so nicely embeddable in the category of Abelian groups, but the Abelian categories are. This suggested a general question, when does an enriched category embed nicely in the enriching category? And Myles had a good description of which Abelian-group enriched categories are Abelian: the exact ones. So the exact category axioms became an approach to this problem. To me this question seems very different from looking for a non-additive analogue of Abelian categories. Am I wrong about that? How did this question look in, say, 1970? How did it look at Dalhousie? Thanks, Colin From rrosebru@mta.ca Fri Dec 7 20:08:52 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:52 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUwk-0001Te-00 for categories-list@mta.ca; Fri, 07 Dec 2001 20:02:26 -0400 Message-ID: From: S.J.Vickers@open.ac.uk To: categories@mta.ca Subject: categories: Two constructivity questions Date: Fri, 7 Dec 2001 10:55:29 -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 Status: O X-Status: X-Keywords: X-UID: 21 Does any one know the answers to these questions? 1. Is trigonometry valid in toposes? (I'll be astonished if it isn't.) 2. Does a polynomial over the complex field C have only finitely many roots? More precisely: 1. Over any topos with nno, let R be the locale of "formal reals", i.e. the classifier for the geometric theory of Dedekind sections. Do sin, cos, arctan, etc. : R -> R exist and satisfy the expected properties? Are there general results (e.g. on power series) that say Yes, of course they do? 2. Consider the space S of square roots of the generic complex number. Working over C, it is the locale corresponding to the squaring map s: C -> C, z |-> z^2. The fibre over w is the space of square roots of w. s is not a local homeomorphism, so S is not a discrete locale. Hence we can't say S is even a set, let alone a finite set in any of the known senses. I don't believe its discretization pt(S) is Kuratowski finite either. If I've calculated it correctly, it is S except for having an empty stalk over zero (oops!), and there is no neighbourhood of zero on which an enumeration can be given of all the elements of pt(S). On the other hand, S is a Stone locale - one can easily construct the sheaf of Boolean algebras that is its lattice of compact opens. That sheaf of Boolean algebras is not Kuratowski finite, nor even, it seems to me, a subsheaf of a Kuratowski finite sheaf. So is there any sense at all in which S is finite? 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 From rrosebru@mta.ca Fri Dec 7 20:08:54 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 07 Dec 2001 20:08:54 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16CUtF-0001z7-00 for categories-list@mta.ca; Fri, 07 Dec 2001 19:58:49 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Thu, 6 Dec 2001 17:43:18 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: categories@mta.ca Subject: categories: Re: Two Days In-Reply-To: <3.0.6.16.20011206082852.4ccf0ab6@pop3.norton.antivirus> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 22 I knew Mahlon Day at Urbana quite well. If he had a mathematician son, I was unaware of it, but you should ask John Gray. Now as far as I know he didn't hire so many category theorists. For example, I was hired by Paul Bateman. So was Jon Beck. As far as I can tell, the only one hired by Mahlon was John Gray. And he may have known Eilenberg, but only as one mathematician may know another. But your entire question is based on a misconception that the hiring at Illinois was based on any sort of plan. The fact is that there was a severe shortage of mathematicians in those days and UI was hiring a couple dozen people a year (and losing a similar number) and anyone who was publishing or well recommended and showed any interest was getting offers. I got at least one utterly unsolicited firm offer from a school I had had no contact with. Possibly, probably, someone like Sammy had given them my name when asked, but that is all. And I received a number of invitations to apply for a job and did and got an offer (and a pay raise from UI). So they didn't even ask what kind of math you did, only that you did some kind of math. Hard to believe what it was like in those days. The people at Illinois who were there for the first midwest category meeting in 1965 were Alex Heller (an algebraic topologist, with an interest in category theory), John Gray (category theorist), Jon Beck (algebraic topology & category theory), Max Kelly (there on a one year leave, category theory), and me (homological algebra). In fact, I wasn't even invited originally; I can thank Max for telling Saunders to invite me. My interest in category theory developed later at the ETH. Now Eckmann is probably the one person most responsible for bringing category theorists together. A history of category theory should talk not only about the founding fathers, but also a certain number of godfathers, people who were not category theorists themselves, but strongly encouraged it. I would include (but not limit it to) Beno Eckmann, Peter Hilton, Alex Heller, David Harrison, .... Of course, there were a number of others who while not primarily category theorists made actual contributions to category theory: Grothendieck, Dan Kan, Albrecht Dold and Dieter Puppe,... Above all, Colin, one should not write a history of category theory without interviewing as many of these people as are still alive and it is damned shame that no one has done this till now. For Eilenberg and Harrison, it is already too late. Michael On Thu, 6 Dec 2001, Colin McLarty wrote: > Working on the history of category theory I find that Mahlon Marsh Day > hired several category theorists at the University of Illinois > Champaign-Urbana in the 1960s. I would like to know whatever people can > tell me about his connections to category theory--perhaps through Eilenberg? > > Also, does anyone here know whether Mahlon Michael Day was Mahlon Marsh > Day's son? Mahlon Michael Day got a PhD at Chicago in 1967 with Kaplansky. > > Thanks, Colin > > > > From rrosebru@mta.ca Sat Dec 8 09:51:26 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 08 Dec 2001 09:51:26 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Chnt-0008EN-00 for categories-list@mta.ca; Sat, 08 Dec 2001 09:46:09 -0400 Date: Sat, 8 Dec 2001 10:22:52 +0000 (GMT) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: Re: Two constructivity questions In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *16CedC-00027r-00*FVUNSPUXi7I* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 23 On Fri, 7 Dec 2001 S.J.Vickers@open.ac.uk wrote: > Does any one know the answers to these questions? > > 1. Is trigonometry valid in toposes? (I'll be astonished if it isn't.) > 2. Does a polynomial over the complex field C have only finitely many roots? > > More precisely: > > 1. Over any topos with nno, let R be the locale of "formal reals", i.e. the > classifier for the geometric theory of Dedekind sections. > > Do sin, cos, arctan, etc. : R -> R exist and satisfy the expected > properties? Are there general results (e.g. on power series) that say Yes, > of course they do? The space of Dedekind reals is Cauchy-complete, so any convergent power series such as sin or cos defines an endomorphism of it. Moreover, provided (as in this case) we can calculate a "modulus of convergense" for the power series explicitly from a bound for x, it's easy to see that the construction x |--> sin x commutes with inverse image functors, so it must be induced by an endomorphism of the classifying topos (that is, of the locale of formal reals). > > 2. Consider the space S of square roots of the generic complex number. > Working over C, it is the locale corresponding to the squaring map s: C -> > C, z |-> z^2. The fibre over w is the space of square roots of w. > > s is not a local homeomorphism, so S is not a discrete locale. Hence we > can't say S is even a set, let alone a finite set in any of the known > senses. I don't believe its discretization pt(S) is Kuratowski finite > either. If I've calculated it correctly, it is S except for having an empty > stalk over zero (oops!), and there is no neighbourhood of zero on which an > enumeration can be given of all the elements of pt(S). > > On the other hand, S is a Stone locale - one can easily construct the sheaf > of Boolean algebras that is its lattice of compact opens. That sheaf of > Boolean algebras is not Kuratowski finite, nor even, it seems to me, a > subsheaf of a Kuratowski finite sheaf. > > So is there any sense at all in which S is finite? > That's a good question. I've never thought about notionss of finiteness for non-discrete locales (someone should!). For the set of points of S, I believe it should be what Peter Freyd called "R-finite" ("R" for "Russell"): intuitively, this means that there is a bound on the size of its K-finite subsets. (However, I don't have a proof of this.) R-finiteness is quite a lot weaker than \tilde{K}-finiteness (being locally a subobject of a K-finite object), but it's still a reasonably well-behaved notion of finiteness (e.g. it is preserved by functors which preserve all finite limits and colimits). Peter Johnstone From rrosebru@mta.ca Sun Dec 9 19:23:42 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 09 Dec 2001 19:23:42 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16DD3b-0001Yu-00 for categories-list@mta.ca; Sun, 09 Dec 2001 19:08:27 -0400 Date: Sun, 9 Dec 2001 15:20:47 +0000 (GMT) From: "Dr. P.T. Johnstone" To: Categories mailing list Subject: categories: Constructive finiteness Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *16D5l3-0003yp-00*2PWaFQC3HiI* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 It is not constructively true, as I conjectured yesterday, that the set of roots of a polynomial over C is Russell-finite. Let X be the subspace of C consisting of 0 and all points whose argument is a rational multiple of \pi, and consider the sheaf of solutions of z^2 - f = 0, where f: X --> C is the inclusion map. It is easy to see that the stalk of this sheaf at 0 is uncountably infinite. Since R-finiteness is preserved by inverse image functors, this yields a counterexample. This doesn't, of course, answer Steve Vickers' original question whether there is a sense in which the *locale* of roots of a polynomial can be said to be finite. But it does indicate that the appropriate notion of finiteness, if it exists, must be a rather delicate one. Peter Johnstone From rrosebru@mta.ca Sun Dec 9 19:23:45 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 09 Dec 2001 19:23:45 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16DD2s-0003xF-00 for categories-list@mta.ca; Sun, 09 Dec 2001 19:07:42 -0400 Message-Id: <3.0.5.32.20011209103526.00854aa0@TESLA.open.ac.uk> X-Sender: sjv22@TESLA.open.ac.uk X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.5 (32) Date: Sun, 09 Dec 2001 10:35:26 +0000 To: categories@mta.ca From: S Vickers Subject: categories: Re: Two constructivity questions In-Reply-To: References: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 25 As before, let S be the Stone locale of square roots of the generic complex number. The question is, In what sense can S be considered finite? Here is one idea that occurs to me. If a set is acted on transitively by a finite group, then classically it must be finite (and I dare say some constructive statement of this is also true). S is acted on by the discrete group {+1, -1} (by multiplication in C). Hence if that action can be considered transitive in some way, that would be a finiteness property of S (or, rather, finiteness _structure_ on S). If a: S x {+1, -1} -> S is the action, then I believe I can prove (by techniques involving the upper powerlocale) that : S x {+1, -1} -> S x S is a proper surjection. This would seem to be a natural way to capture transitivity of a and hence a finiteness property of S. More generally, if an action on a locale by a finite group has only finitely many orbits (using the above idea to specify transitivity on the orbits), then that would be a finiteness property of the locale. One might ask whether, by Galois theory, this can be applied to arbitrary polynomials over C. Steve Vickers. From rrosebru@mta.ca Mon Dec 10 10:17:29 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 10 Dec 2001 10:17:29 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16DRBL-0003Ew-00 for categories-list@mta.ca; Mon, 10 Dec 2001 10:13:23 -0400 Date: Sun, 9 Dec 2001 20:35:20 -0500 (EST) From: JAMES STASHEFF X-Sender: stasheff@login3.isis.unc.edu To: categories@mta.ca Subject: categories: Re: Defining monoids In-Reply-To: <5.1.0.14.2.20011206155739.0204cd50@mail.oberlin.net> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 For those who prefer to see the forests and the trees, that point of view is prominent in the operad/modad/monoidal interaction. Much such material will be in our book on Operads (Markl and Shnider and me) .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 Thu, 6 Dec 2001, Charles Wells wrote: > > > In talking about defining monoids, Toby Bartels wrote: > > "We could also go straight to trees and define them as the basic operations, > then requiring as axiom that grafting of trees produces the same result > as composing the operations." > > This is the mu operation of the corresponding monad. Every single-sorted > "idea" in the sense of the recent discussion generates a monad in sets with > a mu like this. For each set S there is a set of possible computations TS, > a mu:TTS to TS, and a "OneIdentity" operation in the sense of Mathematica > that says the computation consisting of a single node results in that node; > these subject to the monad laws. In other words, the phenomenon you noted > is an instance of a general result. > > --Charles Wells > > 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 > > > > > From rrosebru@mta.ca Wed Dec 12 16:32:20 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 12 Dec 2001 16:32:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16EFzQ-0004Cu-00 for categories-list@mta.ca; Wed, 12 Dec 2001 16:28:29 -0400 From: Chin Wei Ngan Message-Id: <200112121138.TAA20037@sunA.comp.nus.edu.sg> Subject: categories: CFP : ASIA-PEPM 2002 To: categories@mta.ca Date: Wed, 12 Dec 2001 19:38:53 +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 Status: O X-Status: X-Keywords: X-UID: 27 CALL FOR PAPERS ACM SIGPLAN ASIAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation (ASIA-PEPM'02) Aizu, JAPAN, September 12-14 2002 (co-located with FLOPS2002) http://www.comp.nus.edu.sg/asia-pepm02 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 (NTT, 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 (Stanford University, USA) Zhe Yang (University of Pennsylvania, USA) From rrosebru@mta.ca Wed Dec 12 16:32:23 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 12 Dec 2001 16:32:23 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16EFpv-0008RZ-00 for categories-list@mta.ca; Wed, 12 Dec 2001 16:18:39 -0400 Date: Thu, 6 Dec 2001 17:35:59 +0100 Mime-Version: 1.0 (Apple Message framework v472) Content-Type: multipart/alternative; boundary=Apple-Mail-1--715411045 Subject: categories: Positions in Paris 7 University From: Pierre-Louis Curien To: categories@mta.ca Message-Id: <54A7FC46-EA67-11D5-BA7E-003065546D32@pps.jussieu.fr> X-Mailer: Apple Mail (2.472) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 28 Universite Paris 7 - CNRS Laboratoire d'Informatique Algorithmique : Fondements et Applications (LIAFA) Laboratoire Preuves,, Programmes et Systemes (PPS) APPEL A CANDIDATURES / ANNOUNCEMENT Il y aura au concours 2002 / University Paris 7 will hire in 2002 - 2 postes de professeur d'universite / 2 professors - 3 postes de maitres de conferences / 3 assistant professors en informatique / in computer science. La recherche en informatique est repartie sur deux laboratoires / There are two computer science laboratories at Paris 7: - LIAFA (algorithms and combinatorics, automata, modelisation and verification) - PPS (logic and programming) Les deux laboratoires souhaitent renforcer et elargir leurs thematiques / Both laboratories seek to reinforce and enlarge their research themes. Profils recherches / some possible research profiles for applicants - tous les domaines de competence actuels des deux laboratoires / all present themes of LIAFA and PPS - LIAFA: bases de donnees, bio-informatique, cryptographie, ingenierie de la langue, systemes a evenements discrets / data bases, bio-informatics, cryptography, computational linguistics, discrete event systems - PPS: nous recherchons une ouverture sur les objets, ainsi que sur concurrence et mobilite / we seek expertise on objects, and on mobility and concurrency Application information: The positions will be officially open for application in early 2002. Only candidates who have gone through the national Qualification procedure (application during the autumn of year n for applying to a position in year n+1) are eligible. Rather fluent knowledge of French is expected for teaching. The five positions are permanent positions, starting october 2002. Pour plus d'information sur les deux laboratoires / URL links of the two labs http://www.liafa.jussieu.fr http://www.pps.jussieu.fr Contact : Daniel KROB - Directeur du LIAFA - dk@liafa.jussieu.fr Pierre-Louis CURIEN - Directeur de PPS - curien@pps.jussieu.fr From rrosebru@mta.ca Wed Dec 12 16:32:27 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 12 Dec 2001 16:32:27 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16EFvh-0002VR-00 for categories-list@mta.ca; Wed, 12 Dec 2001 16:24:38 -0400 Date: Mon, 10 Dec 2001 21:07:44 -0800 From: Toby Bartels To: categories@mta.ca Subject: categories: Do catgory theorists like philosophy? Message-ID: <20011210210743.A19228@math-cl-n03.ucr.edu> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 [note from moderator: please direct any responses to the poster, thanks] It seems prima facie obvious that category theory ought to attract mathematicians with a philosophical bent, given its potential to revolutionise foundational issues and the perspective on the nature of structure that it affords. But do category theorists interest themselves in aspects of philosophy not directly related to mathematics? I'd be interested to hear from the category theorists on this group, as well as about the category theorists that you know or knew well enough to give a definitive answer. Of course, if ostensibly nonmathematical philosophy ended up having a relation to mathematical philosophy or to category theory itself, that counts too. I hope that this somewhat extracurricular question is not considered out of place, and welcome correction if it is. -- Toby Bartels toby@math.ucr.edu From rrosebru@mta.ca Fri Dec 14 09:01:35 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 14 Dec 2001 09:01:35 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16EriE-0002UY-00 for categories-list@mta.ca; Fri, 14 Dec 2001 08:45:14 -0400 Date: Fri, 14 Dec 2001 12:29:49 +0100 (MET) From: Jiri Adamek X-Sender: adamek@lisa To: categories net Subject: categories: infinite trees Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 30 What is actually a first reference for the fact that for every polynomial endofunctor of Set a final coalgebra consists of all properly labelled (finite and infinite) trees? I suspect the first authors to study this were Arbib and Manes in their "Parametrized data types do not need...", Information and control 52 (1982), 139-158. However, it is obvious from that paper that Arbib and Manes were definitely unaware of the general statement, which explains why they only mention some special cases in their book in 1986. Jiri Adamek xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx From rrosebru@mta.ca Sun Dec 16 18:41:02 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 16 Dec 2001 18:41:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Fjik-0006FQ-00 for categories-list@mta.ca; Sun, 16 Dec 2001 18:25:22 -0400 From: Peter Selinger Message-Id: <200112162206.fBGM6PW27582@quasar.mathstat.uottawa.ca> Subject: categories: Ottawa Logic Group invites graduate student applications To: categories@mta.ca (Categories List) Date: Sun, 16 Dec 2001 17:06:25 -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 Status: O X-Status: X-Keywords: X-UID: 31 Dear colleagues, could you please circulate this announcement to anyone who might be interested, particularly bright prospective graduate students. Thanks, -- Phil, Rick, and Peter The University of Ottawa Logic Group (in the Mathematics Department) is looking for qualified PhD and Master's students. Our group consisting of Richard Blute, Philip Scott, and Peter Selinger, works in a wide range of areas of Logic and theoretical computer science, including: category theory, categorical logic, proof theory, linear logic, type theory, programming language theory, theoretical computer science, and foundations of physics. The Mathematics Department Graduate Program is part of the Ottawa-Carleton Institute of Mathematics and Statistics, and provides a wide range of courses and programs. Ottawa is the capital of Canada, and a beautiful, bilingual (English and French) city, 200 km west of Montreal. Funding for qualified PhD level students in logic is available--an open competition for graduate students will be held in early February. It is also possible to apply to pursue graduate studies with us through SITE (the School of Information Technology and Software Engineering--Computer Science Division), since some of us are cross-appointed in Computer Science. Please enquire. Outside the Mathematics Department, the Logic Group has several other members, including Amy Felty, Tomoyuki Yamakami, and Luigi Logrippo (SITE), Doug Howe and Leopoldo Bertossi (Carleton School of Computer Science), and Mathieu Marion (Philosophy, Ottawa), plus visitors and postdocs. We have a weekly seminar in all areas of logic and in which graduate students are encouraged to present their work. For more information, see: http://quasar.mathstat.uottawa.ca/lfc/ (Logic Group) http://quasar.mathstat.uottawa.ca/grad/ (Graduate Program in Math) Preliminary applications can be completed online, at http://quasar.mathstat.uottawa.ca/grad/apply.html Or for further information, please contact us: Philip Scott scpsg@matrix.cc.uottawa.ca Richard Blute rblute@mathstat.uottawa.ca Peter Selinger selinger@mathstat.uottawa.ca From rrosebru@mta.ca Mon Dec 17 15:06:15 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Dec 2001 15:06:15 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16G2wn-0000tz-00 for categories-list@mta.ca; Mon, 17 Dec 2001 14:57:09 -0400 Date: Fri, 30 Nov 2001 18:19:31 -0800 (PST) From: mjhealy@redwood.rt.cs.boeing.com (Michael Healy 425-865-3123) Message-Id: <200112010219.SAA09113@lilith.rt.cs.boeing.com> To: categories@mta.ca Subject: categories: Change of email address X-Sun-Charset: US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 32 I'm leaving industry to pursue applying category theory in my work---and, incidentally, finally have time to really learn it! My email address from now on is mjhealy@u.washington.edu Regards to all, Mike From rrosebru@mta.ca Mon Dec 17 16:31:20 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 17 Dec 2001 16:31:20 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16G4Oc-0005HS-00 for categories-list@mta.ca; Mon, 17 Dec 2001 16:29:58 -0400 X-Received: from zent.mta.ca ([138.73.101.4]) by mailserv.mta.ca with smtp (Exim 3.33 #2) id 16FzMy-0004t0-00 for rrosebru@mta.ca; Mon, 17 Dec 2001 11:07:56 -0400 X-Received: FROM pragmatix.bangor.ac.uk BY zent.mta.ca ; Mon Dec 17 11:06:25 2001 -0400 X-Received: from hysterix.bangor.ac.uk (hysterix [147.143.2.6]) by pragmatix.bangor.ac.uk (8.9.3+Sun/8.9.3) with ESMTP id PAA29029 for ; Mon, 17 Dec 2001 15:07:53 GMT X-Received: from bangor.ac.uk (maths36 [147.143.10.34]) by hysterix.bangor.ac.uk (8.9.3+Sun/8.9.3) with ESMTP id OAA06912 for ; Mon, 17 Dec 2001 14:57:10 GMT Message-ID: <3C1E07CE.99BB544D@bangor.ac.uk> Date: Mon, 17 Dec 2001 14:57:18 +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: preprint: Multiple categories: the equivalence of a globular anda cubical approach Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 33 This is to advise that a revised version of Title: Multiple categories: the equivalence of a globular and a cubical approach Authors: Fahd A.A. Al-Agl, Ronald Brown and Richard Steiner as accepted today for Advances in Mathematics has been placed on the xArchive at math.CT/0007009. There are some minor but useful corrections and some new pictures. -- Prof 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/ From rrosebru@mta.ca Tue Dec 18 16:21:53 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 Dec 2001 16:21:53 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16GQcO-0002YL-00 for categories-list@mta.ca; Tue, 18 Dec 2001 16:13:40 -0400 Date: Mon, 17 Dec 2001 09:04:59 -0500 (EST) From: larry moss To: cmcs@indiana.edu Subject: categories: CFP: CMCS 02 2nd Call For Papers Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 34 [Apologies for multiple copies] SECOND CALL FOR PAPERS CMCS2002 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: 8 January 2002. 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 From rrosebru@mta.ca Tue Dec 18 16:35:29 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 Dec 2001 16:35:29 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16GQxF-0001P3-00 for categories-list@mta.ca; Tue, 18 Dec 2001 16:35:13 -0400 Date: Mon, 17 Dec 2001 17:26:27 -0500 (EST) From: LICS Message-Id: <200112172226.fBHMQPu08113@moose.cs.indiana.edu> To: categories@mta.ca Subject: categories: job: faculty position in logic Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 35 [Sincere apologies for duplicates] Indiana University invites applications for a tenure-track assistant professor position in applied logic. Please see www.informatics.indiana.edu/positions/logic.html for details. Applications received within the next few weeks are likely to still get full consideration. Applicants are welcome to email to foc@cs.indiana.edu to notify of their mailed application, and to provide pointers to any pertinent on-line documentation. From rrosebru@mta.ca Tue Dec 18 19:36:02 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 Dec 2001 19:36:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16GTkC-0001PH-00 for categories-list@mta.ca; Tue, 18 Dec 2001 19:33:56 -0400 Message-Id: To: categories-list@mta.ca From: "Valeria de Paiva" To: Subject: categories: CFP: IMLA 02 Call for Papers Date: Mon, 17 Dec 2001 14:10:37 PST Message-ID: <001501c18747$a8e40c70$7e10020d@parc.xerox.com> MIME-Version: 1.0 Content-Type: text/plain; charset=3D"iso-8859-1" Content-Transfer-Encoding: 8bit X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook CWS, Build 9.0.2416 (9.0.2910.0) X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4807.1700 Importance: Normal Sender: cat-dist@mta.ca Precedence: bulk [... apologies for multiple copies ... ] ------------------- WORKSHOP ANNOUNCEMENT ----------------------- *** FIRST CALL FOR PAPERS *** FLoC'2002 Workshop IMLA 2: Intuitionistic Modal Logic and Applications '02 http://floc02.diku.dk/IMLA/ July 26, 2002 Copenhagen, Denmark BACKGROUND Constructive and modal logics are of foundational and practical relevance to Computer Science. Constructive logics are used as type disciplines for programming languages, as metalogics for denotational semantics, in the paradigm of program extraction from proofs and for interactive proof development in automated deduction systems such as Agda, Coq, Twelf, Isabelle, HOL, NuPrl and Plastic. Modal logics like temporal logics, dynami= c logics and process logics are used in industrial-strength applications as concise formalisms for capturing reactive behaviour. Although constructive and modal frameworks have typically been investigated separately, a growing body of published work shows that both paradigms can (and should) be fruitfully combined. The goal of this workshop is to stimulate more systematic study of constructive or Intuitionistic Modal Logics and, in parallel of modal type theories. It aims to 1. bring together two largely parallel communities - computer scientists with a focus on proof theory and lambda calculi, and logicians and philosphers with a focus on model theory; 2. bring together theoretically-oriented and the application-oriented approaches, in the hope of productive interaction. Theoretical / methodological issues centre around the question of how the proof-theoretic strengths of constructive logics can best be combined with the model-theoretic strengths of modal logics. Two basic questions are thus "what is the right notion of proof?" and "what is the right way of making a given modal logic constructive?". Topics of interest for papers in the Workshop include, but are not limited to: * applications of intuitionistic necessity or possibility, strong monads, or evaluation modalities, * use of modal type theory to formalize mechanisms of abstraction and refinement, * applications of constructive modal logic and modal type theory to formal verification, abstract interpretation, and program analysis and optimization * applications of modal types to integration of inductive and co-inductive types, higher-order abstract syntax, strong functional programming * computational aspects of the Curry-Howard correspondence between lambda calculi and logics * extensions of this correspondence by other modalities or quantifiers * models of constructive modal logics such as algebraic, categorical= , Kripke, topological, realizability interpretations * notions of proof for constructive modal logics * extraction of constraints or programs, nonstandard information extraction techniques * proof search in constructive modal logic and implementations of it FORMAT The workshop will be an informal one-day meeting with two invited talks, regular paper presentations, and discussion. INVITED SPEAKERS Giovanni Sambin (Padova, Italy) Dana Scott (Pittsburgh, USA) PUBLICATION Workshop contributions must be original work that has not yet appeared elsewhere. If accepted, the authors are expected to present their paper at the workshop. Workshop papers will be made available on the workshop web page and will appear as a technical report handed out to all workshop participants. Authors of accepted papers will be invited to submit full and revised versions of the Workshop papers to a special issue of the Journal of Logic and Computation, for which there will be a second round of refereeing. SUBMISSIONS All submissions should be single column, use 11 point font, and be at most 15 pages in length, preferably using the LaTeX llnc style. Papers should no= t be already published and should not be submitted for simultaneous publication at another conference or workshop. Either send a .ps or .pdf file to M.Mendler@dcs.shef.ac.uk or post a hard copy to Dr Michael Mendler The Department of Computer Science Regent Court 211 Portobello Street Sheffield S1 4DP UNITED KINGDOM by the due date. IMPORTANT DATES IMLA submission deadline: April 5, 2002 IMLA notification : May 23, 2002 IMLA final version : June 20, 2002 PROGRAMME COMMITTEE Natasha Alechina (Nottingham, UK) Sergei Artemov (Cornell, USA) Johan van Benthem (Amsterdam and Stanford) Rajeev Gor=E9 (ANU, Australia) Jean Goubault-Larrecq (ENS-Cachan, France) Michael Mendler (Sheffield ,UK) Eugenio Moggi (Genova, Italy) Valeria de Paiva (Xerox PARC, USA) Frank Pfenning (CMU, USA) Carsten Schuermann (Yale, USA) Alex Simpson (Edinburgh, UK) ORGANISERS Rajeev Gore (ANU, Australia) Michael Mendler (Sheffield, UK) Valeria de Paiva ( PARC, USA) Workshop webpage: http://floc02.diku.dk/IMLA/ From rrosebru@mta.ca Thu Dec 20 13:15:06 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Dec 2001 13:15:06 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16H6kq-0007YJ-00 for categories-list@mta.ca; Thu, 20 Dec 2001 13:13:12 -0400 Message-ID: <20011217221100.25488.qmail@web12203.mail.yahoo.com> Date: Mon, 17 Dec 2001 14:11:00 -0800 (PST) From: Galchin Vasili Subject: categories: multigaphs/categories and constructivism To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 37 Hello, This is another philosophy of math question: 1) What is the constructivist position on infinite multigraphs with loops? 2) What is the constructivist position on infinite categories? Regards, Bill Halchin From rrosebru@mta.ca Thu Dec 20 13:15:09 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Dec 2001 13:15:09 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16H6lN-0000RM-00 for categories-list@mta.ca; Thu, 20 Dec 2001 13:13:45 -0400 Message-Id: To: categories-list@mta.ca Date: Mon, 17 Dec 2001 21:45:57 -0800 (PST) From: Posina Venkata Rayudu Subject: categories: perception to knowledge To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=3Dus-ascii Sender: cat-dist@mta.ca Precedence: bulk Hi, Recently Prof. Lawvere suggested a model for how experimental data lead to theory (see enclosed posting). In this context I would like to mention that there is similar problem in cognitive science. How do we acquire knowledge or how is perceptual experience transformed into conceptual knowledge? Moreover the discussion on generals & particulars readily lends itself to interpretation in cognitive terminology. We may compare particulars with sensation, abstract generals with categories (not the mathematical category) such as =91dog=92, and concrete generals with prototypes. Stretching little further, presentation of abstract general can be compared with percept (of dog). Of all the disciplines to which category theory is applied such as physics or computer science, I think the most natural domain of applications for category theory is cognitive science. Let me explain. Category theory captures mathematical practice. In the domain of mathematics, category theory provides a mathematical account of the process of transforming ignorance into knowledge. It is reasonable to treat the growth of mathematical knowledge as a particular case of knowing in general or cognition. Given that category theory models a particular case of cognition (mathematics), one strategy is to generalize the category theoretic description of the particular case of mathematical knowing to knowing in general or cognition. The ease with which we can implement and realize this research program is inversely proportional to the =91distance=92 between mathematical practice and cognitive processes. The more the cognition is similar to mathematics, the less are the changes or effort we need to make to the category theoretic model of mathematics for it to accommodate cognition in general. In view of the close resemblance between the cognitive process and the pursuit of mathematical knowledge (e.g. both describe real in terms of imaginary), category theoretic study of cognition is likely to be extremely fruitful. One could motivate category theory in more concrete terms. For example, the problem of how perceptual experiences give rise to conceptual knowledge has a facet to which category theory has already provided solution. How do we go from figural or picturesque perception (geometry, topology) to propositional or symbolic thinking (algebra, logic)? Category theory explicated the connections between logic and topology and these insights can be brought to bear on comparable perception-thought transformations, and it possibly gives a cue to the role of thinking vis-=E0-vis perception. =20 I am sorry if I said something really stupid about category theory. I simply want to attract category theorists to cognitive science. Thanking you, Sincerely, Posina Venkata Rayudu =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D From: "F. William Lawvere" =20 To: categories@mta.ca=20 Subject: categories: Re: Sketches and Platonic Ideas=20 Date: Wed, 05 Dec 2001 04:36:21 =20 In my 1972 Perugia Notes I had made an attempt to characterize the relation between these sorts of mathematical considerations and philosophy by saying that while platonism is wrong on the relation between Thinking and Being, something analogous is correct WITHIN the realm of Thinking. The relevant dialectic there is between abstract general and concrete general. Not concrete particular ("concrete" here does not mean "real"). There is another crucial dialectic making particulars (neither abstract nor concrete) give rise to an abstract general; since experiments do not mechanically give rise to theory, it is harder to give a purely mathematical outline of how that dialectic works, though it certainly does work. A mathematical model of it can be based on the hypothesis that a given set of particulars is somehow itself a category (or graph), i.e., that the appropriate ways of comparing the particulars are given but that their essence is not. Then their "natural structure" (analogous to cohomology operations) is an abstract general and the corresponding concrete general receives a Fourier-Gelfand-Dirac functor from the original particulars. That functor is usually not full because the real particulars are infinitely deep and the natural structure is computed with respect to some limited doctrine; the doctrine can be varied, or "screwed up or down" as James Clerk Maxwell put it, in order to see various phenomena. =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 From rrosebru@mta.ca Thu Dec 20 13:15:29 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Dec 2001 13:15:29 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16H6lx-0000yl-00 for categories-list@mta.ca; Thu, 20 Dec 2001 13:14:21 -0400 Message-Id: To: categories-list@mta.ca Date: Wed, 19 Dec 2001 04:09:39 -0800 (PST) From: Posina Venkata Rayudu Subject: categories: language and thinking To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=3Dus-ascii Sender: cat-dist@mta.ca Precedence: bulk Hi, Does the debate -elements and their belongingness vs. functions and their composition- support Sapir-Whorf hypothesis that the way we think is a function of the language we use. In other words, language can transform thinking. According to this doctrine of linguistic relativity, =93users of markedly different grammars are pointed by their grammars toward different types of observations=85and hence are not equivalent as observers, but must arrive at somewhat different views of the world=94 (Whorf 1956, p. 221). Whorf, B. L. (1956) Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf (ed. J. B. Carroll) MIT Press, Cambridge, MA. Thanking you, Sincerely, Posina Venkata Rayudu =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 From rrosebru@mta.ca Thu Dec 20 13:10:17 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Dec 2001 13:10:17 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16H6Zz-0008Vz-00 for categories-list@mta.ca; Thu, 20 Dec 2001 13:01:59 -0400 X-Organisation: Faculty of Science, University of Amsterdam, The Netherlands X-URL: http://www.science.uva.nl/ Date: Wed, 19 Dec 2001 13:58:40 +0100 From: Methods for Modalities To: Methods for Modalities Subject: categories: CFP: HyLo@LICS Message-ID: <20011219135840.A6168@science.uva.nl> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 40 HyLo@LICS 4th WORKSHOP ON HYBRID LOGICS LICS 2002 Affiliated Workshop >>> JULY 25, 2002 <<< Copenhagen, Denmark FIRST CALL FOR PAPERS THEME: Hybrid logic is a branch of modal logic in which it is possible to directly refer to worlds/times/states or whatever the elements of the (Kripke) model are meant to represent. Although they date back to the late 1960s, and have been sporadically investigated ever since, it is only in the 1990s that work on them really got into its stride. It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem (the basic mechanism being to add nominals --- atomic symbols true at a unique point --- together with extra modalities to exploit them) often actually improves the behavior of the underlying modal formalism. For example, it becomes far simpler to formulate modal tableau and resolution in hybrid logic, and completeness and interpolation results can be proved of a generality that is simply not available in modal logic. That is, hybridization --- adding nominals and related apparatus --- seems a fairly reliable way of curing many known weaknesses in modal logic. For more general background on hybrid logic, and many of the key papers, see the Hybrid Logics homepage: http://www.hylo.net HyLo@LICS is likely to be relevant to a wide range of people, including those interested in description logic, feature logic, applied modal logics, temporal logic, and labelled deduction. Moreover, if you have an interest in the work of the late Arthur Prior, note that this workshop is devoted to exploring ideas he first introduced 30 years ago --- it will be an ideal opportunity to see how his ideas have been developed in the intervening period. In this workshop we hope to bring together researchers from all the different fields just mentioned (and hopefully some others) in an attempt to explore what they all have (and do not have) in common. If you're unsure whether your work is of relevance to the workshop, please check out the Hybrid Logics homepage. And do not hesitate to contact the workshop organisers for more information. We'd be delighted to tell you more. Contact details are give below. SUBMISSIONS: We invite the contribution of research papers to the workshop. Please send electronically an extended abstract of up to 10 A4 size pages, in PostScript format to: carlos@science.uva.nl BEFORE the 26st of APRIL, 2002. Please note that all workshop contributors are required by the LICS organizers to register for FLoC 2002. IMPORTANT DATES: Deadline for Submissions: April 26th, 2002 Notification of Acceptance: May 24th, 2002 Deadline for Final Versions: June 25th, 2002 CONTACT DETAILS: Please visit http://www.hylo.net for further information. Send all correspondence regarding the workshop to the organizers: Carlos Areces e-mail: carlos@wins.uva.nl http://www.illc.uva.nl/~carlos Patrick Blackburn e-mail: patrick@coli.uni-sb.de http://www.coli.uni-sb.de/~patrick Maarten Marx e-mail: marx@science.uva.nl http://www.illc.uva.nl/~marx Ulrike Sattler e-mail: sattler@cs.rwth-aachen.de http://www-lti.informatik.rwth-aachen.de/ti/uli-en.html From rrosebru@mta.ca Thu Dec 20 13:10:19 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Dec 2001 13:10:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16H6dp-0000XA-00 for categories-list@mta.ca; Thu, 20 Dec 2001 13:05:57 -0400 Message-Id: To: categories-list@mta.ca Subject: categories: CFP: ICALP2002 From: icalp2002@lcc.uma.es To: categories@mta.ca Message-Id: Date: Wed, 19 Dec 2001 14:39:55 +0100 Sender: cat-dist@mta.ca Precedence: bulk We apologize for possible multiple postings. In http://www.lcc.uma.es/icalp2002 you can find a pdf version of this call for paper. +++++++++++++++++++++++++++++++++++++ Last information: Second version of the WEB pages at http://www.lcc.uma.es/icalp2002 Workshops confirmed: Computability and Complexity in Analysis (CCA 2002) Algorithmic Methods and Models for Optimization of Railways ATMOS 2002 7 th International Workshop on Formal Methods for Industrial Critical Sys= tems Foundations of Wide Area Network Computing Invited speakers confirmed: Heikki Mannila Manuel Hermenegildo +++++++++++++++++++++++++++++++++++++ Call for Papers ICALP 2002=20 29th International Colloquium on=20 Automata, Languages and Programming=20 July 8-13, 2002, M=E1laga, Spain=20 Camera Ready: April 16, 2002 The 29th annual meeting of the European Association of Theoretical Computer Science will be held in M=E1laga, Spain, July 8-13, 2002 (at the E.T.S. Ingenier=EDa Inform=E1tica).=20 As with the Journal Theoretical Computer Science (TCS), the scientific program of the Colloquium will be split into two parts: Track A of the meeting will correspond to Algorithms, Automata, Complexity and Games, while Track B to Logic, Semantics and Theory of Programming.=20 SUBMISIONS: Authors are invited to submit extended abstract of their papers, presenting original contributions to the theory of computer science. Detailed instructions for paper submissions will be found on the conference webpage (http://www.lcc.uma.es/icalp2002) and in future calls for papers. Submissions should consist of: a cover page, with the author's full name, address, fax number, e-mail address, a 100-word abstract, keywords and to which track (A or B) the paper is being submitted and an extended abstract describing original research. At least one author of an accepted paper should be available to present it at the conference. Simultaneous submission to other conferences with published proceedings is not allowed.=20 Further information (dates and instructions for submissions, workshops, registration, location and travel) will be provided in future announcements.=20 ORGANIZING COMMITEE: Buenaventura Clares (University of Granada), Ricardo Conejo (University of M=E1laga), Inmaculada Fortes (University of M=E1laga), Llanos Mora (University of M=E1laga), Rafael Morales (co-Chair, University of M=E1laga), Marlon Nu=F1ez (University of M=E1laga), Jos=E9 Lu= is P=E9rez de la Cruz (University of M=E1laga), Gonzalo Ramos (University of M=E1laga), Francisco Triguero (co-Chair, University of M=E1laga), Jos=E9 Lu= is Trivi=F1o (University of M=E1laga).=20 IMPORTANT DATES:=20 Workshops proposal: November 8, 2001=20 Submissions: January 14, 2002=20 Notification: March 20, 2002=20 CONFERENCE CO-CHAIRS=20 Prof. Francisco Triguero Prof. Rafael Morales=20 Universidad de M=E1laga=20 E.T.S. Ingenier=EDa Inform=E1tica=20 Dept. Lenguajes y Ciencias de la Computaci=F3n=20 Bulevar Louis Pasteur, 35=20 29071 - M=E1laga (SPAIN)=20 e-mail: icalp2002@informatica.uma.es=20 PROGRAM COMMITEE Track A=20 Ricardo Baeza-Yates (U. Chile)=20 Volker Diekert (U. Stuttgart)=20 Paolo Ferragina (U. Pisa)=20 Catherine Greenhill (U. Melbourne)=20 Torben Hagerup (U. Frankfurt)=20 Johan H=E5stad (KTH, Stockholm)=20 Gabriel Istrate (Los Alamos)=20 Claire Kenyon (U. Paris XI)=20 Der-Tsai Lee (Acad. Sinica, Taipei)=20 Heikki Mannila (Nokia, Helsinki)=20 Elvira Mayordomo (U. Zaragoza)=20 Helmut Prodinger (U. Witwatersrand, South Africa)=20 Jan van Leeuwen(U. Utrecht)=20 Paul Vit=E1nyi (CWI, Amsterdam)=20 Peter Widmayer (ETH Z=FCrich) (Chair)=20 Gerhard Woeginger (T.U. Graz)=20 Christos Zaroliagis (U. Patras)=20 Track B=20 Mart=EDn Abadi (Bell Labs Research, Lucent)=20 Roberto Amadio (U. Provence)=20 Gilles Barthe (INRIA-SophiaAntipolis)=20 Manfred Droste (University of Technology Dresden)=20 C=E9dric Fournet (Microsoft Cambridge)=20 Matthew Hennessy (U. Sussex) (Chair)=20 Furio Honsell (U. Udine)=20 Peter O'Hearn (Queen Mary & W. C. London)=20 Fernando Orejas (U.P.Catalunya)=20 Ernesto Pimentel (U. M=E1laga)=20 David Sands (Chalmers University of Technology and G=F6teborg University)= =20 Dave Schmidt (U. Kansas)=20 Gheorghe Stefanescu (U. Bucharest)=20 Vasco Vasconcelos (U. Lisbon)=20 Thomas Wilke (U. Kiel) +++++++++++++++++++++++++++++++++++++++++++ Malaga University uses Christmas holidays for backup and maintenance of his= network. If you have problem to arrive to ICALP 2002 main page, please retry again l= ater. If you get to the page http://www.lcc.uma.es but not to the page http://www= =2Elcc.uma.es/icalp2002 contact with us: conejo@lcc.uma.es morales@lcc.uma.es From rrosebru@mta.ca Thu Dec 20 20:21:54 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Dec 2001 20:21:54 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16HDMQ-0000AX-00 for categories-list@mta.ca; Thu, 20 Dec 2001 20:16:26 -0400 X-Received: from zent.mta.ca ([138.73.101.4]) by mailserv.mta.ca with smtp (Exim 3.33 #2) id 16H9b4-0005ZS-00 for cat-dist@mta.ca; Thu, 20 Dec 2001 16:15:18 -0400 X-Received: FROM server01.oberlin.net BY zent.mta.ca ; Thu Dec 20 16:12:39 2001 -0400 X-Received: from wells.freude.com (ip-184-208.oberlin.net [216.111.184.208]) by server01.oberlin.net (8.9.3/8.9.3) with ESMTP id PAA24926 for ; Thu, 20 Dec 2001 15:11:49 -0500 (EST) Message-Id: <5.1.0.14.2.20011220150640.0206d300@mail.oberlin.net> X-Sender: cwells@mail.oberlin.net X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Thu, 20 Dec 2001 15:17:01 -0500 To: cat-dist@mta.ca From: Charles Wells Subject: categories: Re: language and thinking In-Reply-To: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 42 Learning category theory (which I did after I wrote a dissertation and several papers in finite fields) certainly changed and improved the way I did mathematics. The change indeed deserves to be called a transformation. In a similar way, my ability to program in Basic improved remarkably when I learned the basic ideas of structured programming and did a little programming in Pascal. But I am reasonably sure that these transformations in my thinking occurred because I learned important new concepts such as limit, adjoint, while-loop, etc. Learning new concepts transforms one's thinking. I am not a linguist, but I know something of Whorf's ideas; I don't understand how one can disentangle the effect of knowing the different concepts that different cultures have from the effect of knowing their language. This brings up the question: Can concepts be differentiated from language? I say via introspection that the answer is "certainly", because when I concentrate on a mathematical problem (or how to reassemble a machine or write a complicated program) the "talking" in my head goes away and is replaced by pictorial concepts located in mental space. Some people claim that this never happens to them. If that is true, it would appear that people come in two different varieties, from Mars and from Venus maybe. But I suspect that the people who claim it never happens are simply wrong: they lack sufficient introspective ability. --Charles Wells >Does the debate -elements and their belongingness vs. >functions and their composition- support Sapir-Whorf >hypothesis that the way we think is a function of the >language we use. In other words, language can >transform thinking. According to this doctrine of >linguistic relativity, =93users of markedly different >grammars are pointed by their grammars toward >different types of observations=85and hence are not >equivalent as observers, but must arrive at somewhat >different views of the world=94 (Whorf 1956, p. 221). > >Whorf, B. L. (1956) Language, Thought, and Reality: >Selected Writings of Benjamin Lee Whorf (ed. J. B. >Carroll) MIT Press, Cambridge, MA. > >Thanking you, >Sincerely, >Posina Venkata Rayudu > >=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 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 From rrosebru@mta.ca Fri Dec 21 09:27:02 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 21 Dec 2001 09:27:02 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16HPf1-0006CO-00 for categories-list@mta.ca; Fri, 21 Dec 2001 09:24:27 -0400 X-Received: from zent.mta.ca ([138.73.101.4]) by mailserv.mta.ca with smtp (Exim 3.33 #2) id 16HMZ3-0002Dn-00 for cat-dist@mta.ca; Fri, 21 Dec 2001 06:06:05 -0400 X-Received: FROM mercury.open.ac.uk BY zent.mta.ca ; Fri Dec 21 06:03:26 2001 -0400 X-Received: from moray.open.ac.uk by mercury.open.ac.uk via SMTP Local (Mailer 3.1) with ESMTP; Fri, 21 Dec 2001 10:05:50 +0000 X-Received: by moray.open.ac.uk with Internet Mail Service (5.5.2653.19) id ; Fri, 21 Dec 2001 10:05:48 -0000 Message-ID: From: S.J.Vickers@open.ac.uk To: categories@mta.ca Subject: categories: Re: language and thinking Date: Fri, 21 Dec 2001 10:05:48 -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 Status: O X-Status: X-Keywords: X-UID: 43 > This brings up the question: Can concepts be differentiated from language? Two quite different examples: first, a very practical one. This is of vital importance in teaching computing. Programming languages come and go, and to be reasonably future-proof a programming course must go beyond merely "teaching a programming language" and bring out concepts. Some evidence that concepts can be differentiated from language is seen in the graphical Integrated Development Environments (IDEs) for developing object oriented programs. For instance, if you compare those for Java with those for C++ you find that broadly similar 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. This sounds very like Charles's replacement of talking in his head by pictorial concepts. Its effectiveness in IDEs is indisputable, and it seems to be because the language by itself in some way hobbles your thought processes (cf. Basic programming improved by knowing Pascal). A quite different example is that of foundations, how choice of logic affects what you can recognize as mathematics. But don't get me going on that. Merry Christmas, Steve Vickers. From rrosebru@mta.ca Sat Dec 22 10:41:00 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 22 Dec 2001 10:41:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16Hn8f-00077E-00 for categories-list@mta.ca; Sat, 22 Dec 2001 10:28:37 -0400 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15395.22395.395902.354072@chtapach.loria.fr> Date: Fri, 21 Dec 2001 16:38:35 +0100 (MET) From: Christophe Ringeissen To: categories@mta.ca Subject: categories: CFP: AMAST'2002 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 Status: O X-Status: X-Keywords: X-UID: 44 [We apologize if you receive multiple copies of this message] 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 From rrosebru@mta.ca Sat Dec 29 20:19:24 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 29 Dec 2001 20:19:24 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16KTal-0002ex-00 for categories-list@mta.ca; Sat, 29 Dec 2001 20:12:43 -0400 Date: Wed, 26 Dec 2001 09:06:43 -0500 (EST) From: Peter Freyd Message-Id: <200112261406.fBQE6hH19209@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Two categories or 2-categories? Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 45 In the film "A Beautiful Mind," the first indication that John Nash is regaining his abilities is a conversation with a student ("Galois extensions are really the same as covering spaces!" exclaims Toby, the student). The scene ends with Nash and the student bent over some papers and -- as I heard it -- the student says: "Functor...Two...Categories" (The film's not bad but its relation to Nash's life is tangential. If I had not absorbed a hint from a review, I think I might have stomped out in the middle because of the ridiculous portrayal of what mathematicians do. It turns out that the filmmakers are playing a game -- very effective with most of the audience -- in sliding between perceptions: ours and Nash's.) From rrosebru@mta.ca Sat Dec 29 20:19:27 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 29 Dec 2001 20:19:27 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16KTZe-0008Tm-00 for categories-list@mta.ca; Sat, 29 Dec 2001 20:11:34 -0400 To: categories@mta.ca Subject: categories: Enriched locally presentable categories From: Mark Hovey Date: 26 Dec 2001 07:18:19 -0500 Message-ID: Lines: 24 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 Status: O X-Status: X-Keywords: X-UID: 46 I am still trying to understand some enriched category theory. Suppose V is a closed symmetric monoidal category that is also locally presentable. Suppose C is a small V-category. I am interested in the category of V-functors from C to V, and, in particular, I want to know that it is locally presentable. Might need some hypotheses on C for this, but I would prefer to avoid hypotheses on the actual functors. This time I have actually looked in Kelly's book and I did not see it, but I confess to finding this subject rough going so might have missed it. On the other hand, my library is closed for the holiday, so I have not looked at Adamek and Rosicky's book on enriched category theory yet. I guess the generators ought to be the representable functors. I know everything is a weighted colimit of representables, but I don't know whether this colimit is filtered enough, nor do I know whether one can get away with weighted colimits instead of ordinary ones. One direction this might go is to develop a theory of locally presentable in an enriched sense, using weighted colimits instead of colimits. I would prefer to avoid that if possible. Happy holidays to all. Mark Hovey From rrosebru@mta.ca Mon Dec 31 10:55:38 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 10:55:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16L3l0-0005n4-00 for categories-list@mta.ca; Mon, 31 Dec 2001 10:49:42 -0400 Date: Mon, 31 Dec 2001 19:30:27 +1100 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Message-Id: <200112310830.fBV8URA305918@milan.maths.usyd.edu.au> To: categories@mta.ca Subject: categories: Re: Enriched locally presentable categories Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 47 Mark Hovey's letter of 26 Dec - known as Boxing Day in the British-speaking world - suggests that it might be a good idea to develop a theory of local presentability and all that in the context of enriched categories. In fact such a theory was developed in my paper [Structures defined by finite limits in the enriched context I, Cahiers de Top. et Geom. Differentielles 23 (1982), 3 - 42]. Everything works very smoothly; but there are a few annoying misprints, many of which seem to be my own fault. Further developments can be found in [Blackwell-Kelly-Power, Two-dimensional monad theory, J. Pure Appl. Algebra 59 (1989), 1 - 41] and in [Kelly-Power, Adjunctions whose counits are coequalizers and presentations of finitary enriched monads, J. Pure Appl. Algebra 89 (1993), 163 - 179], among other papers of myself and of others; Brian Day, Steve Lack, John Power, and Ross Street have all written on related matters. Please accept, Mark, my best wishes for your future work in this direction. In any case, New Year's Eve is a fine time to send greetings more generally to Bob and all on this Bulletin Board. Warm regards - Max Kelly. From rrosebru@mta.ca Mon Dec 31 10:55:41 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 10:55:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16L3n4-0000Yh-00 for categories-list@mta.ca; Mon, 31 Dec 2001 10:51:50 -0400 Message-ID: <000b01c191d5$8cc90390$0e034ed4@WALTER> From: "RFC Walters" To: Subject: categories: New address: RFC Walters Date: Mon, 31 Dec 2001 09:31:29 +0100 MIME-Version: 1.0 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 Status: RO X-Status: X-Keywords: X-UID: 48 New email address robert.walters@uninsubria.it New mail address Universita' dell'Insubria Dipartimento di Scienze CC, FF e MM Via Valleggio 11 22100 COMO, Italy Web homepage http://www.unico.it/~walters/ My recent papers are available there: the latest being P. Katis, N. Sabadini, R.F.C. Walters Feedback, trace and fixed point semantics We introduce a notion of category with feedback-with-delay, closely related to the notion of traced monoidal category, and show that the Circ construction of [JPAA 115: 141--178, 1997] is the free category with feedback on a symmetric monoidal category. Combining with the Int construction of Joyal-Street-Verity [Math. Proc. Camb.Phil. Soc., 119, 447-468, 1996] we obtain a description of the free compact closed category on a symmetric monoidal category. We thus obtain a categorical analogue of the classical localization of a ring with respect to a multiplicative subset. In this context we define a notion of fixed-point semantics of a category with feedback which is seen to include a variety of classical semantics in computer science. Others: R. Rosebrugh, N. Sabadini, R. F. C. Walters, Minimization and Minimal Realization in Span(Graph), submitted P. Katis, N. Sabadini, RFC Walters, Classes of finite state automata for which compositional minimization is linear time Fabio Gadducci, Piergiulio Katis, Ugo Montanari, Nicoletta Sabadini, Robert F.C. Walters, Comparing cospan-spans and tiles via a Hoare-style process calculus From rrosebru@mta.ca Mon Dec 31 10:55:41 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 10:55:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16L3ob-0003up-00 for categories-list@mta.ca; Mon, 31 Dec 2001 10:53:25 -0400 X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Mon, 31 Dec 2001 09:21:38 -0500 (EST) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: Natural disasters Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 49 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 From rrosebru@mta.ca Mon Dec 31 10:55:44 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 10:55:44 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16L3oB-0008DV-00 for categories-list@mta.ca; Mon, 31 Dec 2001 10:52:59 -0400 Date: Mon, 31 Dec 2001 19:55:56 +1100 (EST) From: maxk@maths.usyd.edu.au (Max Kelly) Message-Id: <200112310855.fBV8tun306897@milan.maths.usyd.edu.au> To: categories@mta.ca Subject: categories: Re: Two categories or 2-categories? Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 50 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. From rrosebru@mta.ca Mon Dec 31 21:02:41 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 21:02:41 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16LDCf-00009W-00 for categories-list@mta.ca; Mon, 31 Dec 2001 20:54:53 -0400 Subject: categories: Re: Natural disasters From: Duraid Madina To: Categories list In-Reply-To: References: Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Mailer: Evolution/1.0 (Preview Release) Date: 01 Jan 2002 04:08:24 +1200 Message-Id: <1009814905.90809.0.camel@simplex.idesign.fl.net.au> Mime-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 51 The fires here in Sydney are still blazing away, but that didn't stop the new year's fireworks display from going ahead just a few hours ago. As far as I am aware, no (human) lives have been lost, but there's been a great deal of property damage, and an immense amount of national parkland has been burned away. In truth, most Sydneysiders are unaffected except for the appalling air quality and the fact that a fine layer of ash has been deposited over the entire city, which people will no doubt discover on their desks as they return to work! You can take a look at some eerie pictures of the Sydney skyline here: http://www.smh.com.au/news/0112/26/gallery/snapshot1.html Duraid On Tue, 2002-01-01 at 02:21, 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 > From rrosebru@mta.ca Mon Dec 31 21:02:44 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 21:02:44 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16LDDH-0005Bp-00 for categories-list@mta.ca; Mon, 31 Dec 2001 20:55:31 -0400 From: baez@math.ucr.edu Message-Id: <200112311647.fBVGlLL06385@math-cl-n05.ucr.edu> Subject: categories: Two categories or 2-categories To: categories@mta.ca (categories) Date: Mon, 31 Dec 2001 08:47:21 -0800 (PST) In-Reply-To: <200112310855.fBV8tun306897@milan.maths.usyd.edu.au> from "Max Kelly" at Dec 31, 2001 07:55:56 PM 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 Status: RO X-Status: X-Keywords: X-UID: 52 Max Kelly writes: > 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 forget who said what, but I think the issue was that when folks are talking in this movie, you can't easily tell whether they are saying "2-categories" or "two categories", i.e. a couple of categories. This problem comes up a lot in my life, and I am glad to see it finally showing up in a major motion picture! E.g., I must be careful never to say "functor between two categories", replacing it by "functor from one category to another". I would be shocked if they were talking about 2-categories in this movie. Even mentioning categories must seriously diminish their ticket sales, much less 2-categories. On a wholly different note, how are the category theorists in Sydney?