From rrosebru@mta.ca Thu Feb 2 05:31:09 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 02 Feb 2006 05:31:09 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F4aiS-0003LF-6l for categories-list@mta.ca; Thu, 02 Feb 2006 05:25:24 -0400 Subject: categories: Re: horizontal composition (fwd) To: categories@mta.ca Date: Wed, 1 Feb 2006 13:13:42 -0400 (AST) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: <20060201171343.1668C73676@chase.mathstat.dal.ca> From: rjwood@mathstat.dal.ca (RJ Wood) Sender: cat-dist@mta.ca Precedence: bulk X-IMAPbase: 1144781879 37 Status: RO X-Status: X-Keywords: X-UID: 1 Jean Benabou seems to have invented so many things but, like Al Gore, he did not invent the internet. He seems to have difficulty with upper and lower case letter issues. If objects are denoted by upper case then in in email text it is a reasonable convention to use lower case for 1-cells, upper case for 2-cells, and so on. He should also be told that ordinary words written in upper case are understood to be SHOUTED. (Most of us do not read anything that is shouted.) Rj Wood I thought I had invented bicategories in 1967, and that, at the very=20= beginning of the paper, in =A71, I had defined the two composition laws=20= and drawn pictures to explain them. Of course I denoted by capital=20 letters the 1-cells, thinking of functors, and by small letters the=20 2-cells, thinking of natural transformations. That certainly makes a=20 tremendous difference with Susan Niefield's notation who uses the=20 converse convention and amply justifies Marco Grandis in giving=20 references dated 1994 and 1996, i.e. more than 25 years posterior to my=20= original paper. With best regards > > You can find the strict version of that result in Prop. 1.4 of > > - M. Grandis, Homotopical algebra in homotopical categories, Appl.=20 > Categ. > Structures 2 (1994), 351-406. > > I do not know if it has been written down elsewhere. > > For sure, whiskering of natural transformations with functors is used=20= > in: > > - R. Street, Categorical structures, in: Handbook of Algebra, Vol. 1,=20= > 529-577, > North Holland, Amsterdam 1996. > > where you can find the notion of a sesqui-category (which does not=20 > assume the > "reduced interchange axiom" you are mentioning). > > With best regards > > M. Grandis > >> >> Does anyone know of a reference for the following definition of a >> bicategory? The primitive composites are: >> >> gf for composable 1-cells >> GF for vertically composable 2-cells >> f*G and F*g for horizontally composable pairs of each >> >> with appropriate axioms including (G*f')(g*F)=3D(g'*F)(G*f), for >> F:f->f':X->Y and G:g->g':Y->Z. The horizontal composite G*F is=20 >> defined to >> be the common value of the two vertical composites. >> >> -Susan > > > From rrosebru@mta.ca Thu Feb 2 05:31:09 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 02 Feb 2006 05:31:09 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F4alP-0003P5-OY for categories-list@mta.ca; Thu, 02 Feb 2006 05:28:27 -0400 Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit From: Marco Grandis Subject: categories: Re: horizontal composition Date: Thu, 2 Feb 2006 08:15:45 +0100 To: categories@mta.ca X-Mailer: Apple Mail (2.746.2) Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 2 Dear Jean (and dear colleagues), Everyone knows you defined bicategories (and Charles Ehresmann 2- categories). The point of those two messages is that one can equivalently define a 2-category or a bicategory using the following primitive operations (and suitable axioms): - the vertical composition of cells, - the whisker composition of cells with maps (instead of the horizontal composition of cells). (Which is precisely what we concretely do in Cat, when we define horizontal composition of natural transformations: we use vertical composition and whiskering, showing that the two possible ways of defining horizontal composition give the same result, by the relevant part of the middle-four interchange axiom - which I was calling "reduced interchange".) All this has some importance in homotopy, which is why I was interested in it. For instance, take chain complexes with their homotopies: then the vertical composition of homotopies is (strictly) associative, whiskering is also associative (in the appropriate sense), but reduced interchange fails and you do not have a horizontal composition of homotopies. Such a structure is a sesqui- category in Ross Street's sense - actually one might say "sesqui- groupoid". With best regards Marco From rrosebru@mta.ca Tue Feb 7 09:41:19 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 07 Feb 2006 09:41:19 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F6SvT-0006Jw-74 for categories-list@mta.ca; Tue, 07 Feb 2006 09:30:35 -0400 From: "Noson Yanofsky" To: "categories@mta. ca" Subject: categories: Towards a Definition of an Algorithm Date: Mon, 6 Feb 2006 17:22:44 -0500 Content-Type: text/plain;charset="US-ASCII" Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 3 Dear All, I just put a paper up at http://arxiv.org/abs/math/0602053 . It should be of interest to many. It uses coherence rules to tell when two programs are essentially the same algorithm. Here is the title and abstract: Towards a Definition of an Algorithm We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are ``essentially'' the same program. The set of all equivalence classes is the category of all algorithms. In order to explore these ideas, the set of primitive recursive functions is considered. Each primitive recursive function can be described by many labeled binary trees that show how the function is built up. Each tree is like a program that shows how to compute a function. We give relations that say when two such trees are ``essentially'' the same. An equivalence class of such trees will be called an algorithm. Universal properties of the category of all algorithms are given. Looking forward to hearing any thoughts and criticisms. I hope to see you all in Nova Scotia at CT 2006 this Summer! All the best, Noson (Yanofsky) From rrosebru@mta.ca Wed Feb 8 17:13:24 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 08 Feb 2006 17:13:24 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F6wUl-0006ch-9Q for categories-list@mta.ca; Wed, 08 Feb 2006 17:04:59 -0400 From: Jurgen Koslowski Subject: categories: PSSL in Braunschweig, Preliminary announcement To: categories@mta.ca (categories list) Date: Tue, 7 Feb 2006 17:56:58 +0100 (CET) MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 4 Dear All, PSSL 84 - preliminary announcement http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/PSSL84.html The 84th meeting of the seminar will be held at the Department of Theoretical Computer Science of the Technical University in Braunschweig, Germany, over the weekend of October 14/15, 2006. The seminar welcomes talks using or addressing category theory or logic, either explicitly or implicitly, in the study of any aspect of mathematics or science. This will be a fairly informal affair,=20 presentations of work in progress are quite acceptable. Braunschweig is located about 60 km East of Hannover and can easily be reached by car or train. The closest airport is in Hannover. Since Expo 2000, there is a fast train connection from that airport to Hannover's main train station. Trains to Braunschweig leave at least=20 once every hour and take about 40 minutes or less. =20 Further information will become available on the web-page listed above, where you can also register on-line. Jiri Adamek Juergen Koslowski Stefan Milius Juergen Koslowski If I don't see you no more on this world ITI, TU Braunschweig I'll meet you on the next one koslowj@iti.cs.tu-bs.de and don't be late! http://www.iti.cs.tu-bs.de/~koslowj Jimi Hendrix (Voodoo Child, SR) From rrosebru@mta.ca Wed Feb 8 17:13:25 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 08 Feb 2006 17:13:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F6wWN-0006lE-6Y for categories-list@mta.ca; Wed, 08 Feb 2006 17:06:39 -0400 Date: Wed, 08 Feb 2006 16:16:35 +0100 From: Urs Schreiber To: categories@mta.ca Subject: categories: special ambidextrous adjunctions? Content-Type: text/plain; charset=ISO-8859-15; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 5 While making a web search I came across an old message by Paul Levy. He had originally asked (in message 200111201650.fAKGol115859@foobar.pps.jussieu.fr ): > If P and Q are objects in a 2-category C, and there is an equivalence > between them, must there be an adjoint equivalence (an adjunction > whose unit and counit are both isomorphisms) between them?" After the answer was given he revealed the motivation for his question: > I'm trying to make an argument that the natural 2-categorical > analogue of isomorphism is adjoint equivalence rather than > equivalence, but your result suggests that it doesn 't matter. I am currently wondering about a closely related observation. While playing around with the notion of 2-transport, I noticed that, contrary to my original assumption, in order for a certain 2-functor to be expressible in terms of another 2-functor (to be "locally trivializable" in my application) it suffices for both 2-functors to be related by a "special ambidextrous adjunction". By a special ambidextrous adjunction I mean an ambidextrous adjunction A --L--> B -- R --> A such that 1 ==> LR ==> 1 and 1 ==> RL ==> 1 are identity 2-morphisms. This is strictly weaker than an adjoint equivalence. (I have chosen the adjective "special" in order to allude to the fact that the Frobenius algebras obtained from these adjunctions are called "special Frobenius algebras".) I would like to know if there are any well known insights concerning such "special ambidextrous adjunctions". P.S. There are notes with more details and examples here: http://www.math.uni-hamburg.de/home/schreiber/FRSfrom2Transport.pdf From rrosebru@mta.ca Wed Feb 8 17:13:25 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 08 Feb 2006 17:13:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F6wVm-0006hq-J3 for categories-list@mta.ca; Wed, 08 Feb 2006 17:06:02 -0400 From: Thomas Streicher Subject: categories: Question (fwd) To: categories@mta.ca Date: Wed, 8 Feb 2006 15:58:31 +0100 (CET) MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 6 My colleague Klaus Keimel has the following question and would be glad if someone could answer it. If you want to answer him directly his e-mail address is keimel@mathematik.tu-darmstadt.de I have come across a different, but similar question concerning the distribution monad on Froelicher spaces (as studied by Froelicher, Kriegl and Michor). Can one characterize elementarily the algebras for the monad T(X) = Lin(R^X,R) on \SS, the cartesian closed category of Froelicher spaces and "smooth" maps between them? I guess smooth and linear is not sufficient... Thomas Streicher ----------------------------------------------------------------------- The monad of probability measures over compact Hausdorf spaces If we assign to every compact Hausdorff space X the set PX of all probability measures on X endowed with the vague (= weak*topology if we consider PX embedded in the dual of C(X)), then we have a monad. The unit e assign the Dirac measure to every point x in X, the multiplication m assigns the barycentre of every probability measure on PX. My question is: What are the algebras and the algebra homomorphisms of this monad? It should be straightforward, that compact convex sets in locally convex vector spaces are algebras. Probability measures on such spaces have a barycentre. Continuous affine maps should be homomorphisms. Are these all algebras and homomorphisms? One thinks that this should be known. Who knows about this? I would be interested in hints and in relevant references. Klaus Keimel From rrosebru@mta.ca Wed Feb 8 17:13:25 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 08 Feb 2006 17:13:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F6wXB-0006qe-MD for categories-list@mta.ca; Wed, 08 Feb 2006 17:07:29 -0400 Date: Wed, 08 Feb 2006 16:10:34 +0100 From: Frank Ciesinski To: categories@mta.ca Subject: categories: CONCUR 2006 Call for Papers MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 7 --------------------------------------------------------------- Apologies if you received multiple copies of this announcement. --------------------------------------------------------------- CALL FOR PAPERS CONCUR'06 17th International Conference on Concurrency Theory August 27th - 30th, 2006 Bonn, Germany http://depend.cs.uni-sb.de/concur06 CONCUR 2006, the 17th International Conference on Concurrency Theory, will take place in Bonn, Germany, August 27 - 30, 2006. The purpose of the CONCUR conferences is to bring together researchers working on the theory of concurrency and its applications. Submissions are solicited in all areas of semantics, logics, and verification techniques for concurrent systems. The principal topics include (but are not limited to): * Basic models and logics of concurrent and distributed computation (such as process algebras, Petri nets, domain theoretic or game theoretic models, modal and temporal logics). * Specialized models or classes of systems (such as circuits, synchro- nous systems, real time and hybrid systems, stochastic systems, data bases, mobile and migrating systems, parametric protocols, security protocols). * Related verification techniques and tools (such as state-space ex- ploration, model-checking, synthesis, abstraction, automated de- duction, testing). * Related programming models (such as distributed, constraints or ob- ject oriented, graph rewriting, as well as associated type systems, static analyses, abstract machines, and environments). Authors are invited to submit an extended abstract; submissions will be evaluated by the program committee for inclusion in the pro- ceedings, which will be published by Springer-Verlag in the Lecture Notes in Computer Science series. Papers must contain original con- tributions, be clearly written, and include appropriate reference to and comparison with related work. Simultaneous submission to journals or other conferences with published proceedings is not allowed. Authors are required to submit a paper title and a short abstract be- fore submitting the extended abstract. The short abstract should not exceed 200 words, and it should be entered in ASCII at the conference web site. The extended abstract should not exceed 15 pages, and it should be formatted according to Springer-Verlag LNCS guidelines. If necessary, the extended abstract may be supplemented with a clearly marked appendix, which will be reviewed at the discretion of the pro- gram committee. The link for submission will be available at the web- site: http://depend.cs.uni-sb.de/concur06 Invited Speakers ================ * Jan-Willem Klop, Free University of Amsterdam, The Netherlands * Orna Kupferman, Hebrew University, Israel * Edward A. Lee, University of California at Berkeley, USA Invited Tutorials by ==================== * Uwe Nestmann, Technical University of Berlin, Germany * Roberto Segala, University of Verona, Italy Important Dates =============== Abstract Submission: March 23, 2006 Paper Submission: April 3, 2006 (STRICT) Notification: May 20, 2006 Final version due: June 9, 2006. Affiliated Workshops ==================== Eleven workshops will be affiliated with CONCUR 2006: FMICS, INFINITY, EXPRESS, SOS, GETCO, GVD, FOCLASA, PDMC, SecCo, CORTOS, GT-VC. CONCUR Steering Committee ========================= Roberto Amadio, University of Paris 7, France, Jos Baeten, Eindhoven University of Technology, the Netherlands, Eike Best, University of Oldenburg University, Germany, Kim Larsen, Aalborg University, Denmark, Ugo Montanari, University of di Pisa, Italy, Scott Smolka, SUNY Stony Brook, USA. Program Committee Chairs ======================== Christel Baier, University of Bonn, Germany, Holger Hermanns, University of Saarland, Germany Program Committee ================= Parosh Abdulla Uppsala University, Sweden Luca Aceto Reykjavik University, Iceland Luca de Alfaro University of California, Santa Cruz, USA Roberto Amadio University of Paris 7, France Jos Baeten Eindhoven University of Technology, the Nether- lands Christel Baier University of Bonn, Germany Patricia Bouyer Ecole Normale Superieure de Cachan, France Franck van Breugel York University, Canada Kousha Etessami University of Edinburgh, United Kingdom Wan Fokkink Free University of Amsterdam, the Netherlands Philippa Gardner Imperial College London, United Kingdom Rob van Glabbeek The University of New South Wales, Australia Holger Hermanns University of Saarland, Germany Barbara Koenig University of Stuttgart, Germany Antonin Kucera Masaryk University in Brno, Czeck Republic Kim Larsen Aalborg University, Denmark Gerald Luettgen University of York, United Kingdom Nancy Lynch Massachusetts Institute of Technology, USA Massimo Merro University of Verona, Italy Ugo Montanari University of Pisa, Italy Anca Muscholl University of Paris 7, France Catuscia Palamidessi INRIA Futurs Saclay, France Woijtek Penczek University of Podlasie, Poland Corrado Priami University of Trento, Italy Jean-Francois Raskin Universite Libre de Bruxelles, Belgium Jan Rutten CWI, The Netherlands PS Thiagarajan National University of Singapore, Singapore From rrosebru@mta.ca Thu Feb 9 21:46:40 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Feb 2006 21:46:40 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F7NEt-0001CC-6o for categories-list@mta.ca; Thu, 09 Feb 2006 21:38:23 -0400 Date: Wed, 8 Feb 2006 22:51:35 -0600 (CST) From: Eugenia Cheng To: categories@mta.ca Subject: categories: Mac Lane Conference: second announcement Message-ID: 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: 8 Dear all, This is the second announcement for the conference in memory of Saunders Mac Lane, at the University of Chicago, April 7 through April 11 2006. The conference will be on "Category Theory and its Applications". NEW: NSF funding is now available for students and postdocs. See below for details. For the text of the first announcement, and further details, including the schedule of speakers and travel information, please see http://www.math.uchicago.edu/~may/MACLANE or http://www.math.uchicago.edu/~eugenia/maclane. This will be an informal conference with no registration fee. Talks will take place in the Mathematics Department building (Eckhart Hall). There will be an informal lunch and reception arranged after the memorial service on Friday, April 7; for other meals, attendees can choose from a variety of options on and around campus. Accommodation near campus is limited. We have reserved a block of rooms at the Ramada Inn at a special conference rate of $95 per night (plus tax). To reserve one of these rooms please call +1-773-288-5000 during CST office hours, and mention the Mac Lane Memorial Conference. Please note that these rooms will be released to the general public on March 6. The hotel website is at http://www.ramada-chicago.com. FUNDING FOR STUDENTS AND POSTDOCS Funding for this conference has been made available by the NSF. If you are a student or postdoc and would like to be considered for financial support, please send your name, institution, and, if you are a student, the name of your advisor to Eugenia Cheng by February 28. GENERAL REGISTRATION If you plan to attend this conference or have any further questions, please e-mail Eugenia Cheng at the above address (eugenia@math.uchicago.edu). We look forward to seeing you in April. With best regards, The organisers Peter May Eugenia Cheng From rrosebru@mta.ca Thu Feb 9 21:46:40 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Feb 2006 21:46:40 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F7NDB-00014o-PA for categories-list@mta.ca; Thu, 09 Feb 2006 21:36:37 -0400 Mime-Version: 1.0 (Apple Message framework v623) To: "categories@mta. ca" From: Marquis Jean-Pierre Subject: categories: Fwd: Voevodsky Date: Wed, 8 Feb 2006 22:29:21 -0500 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain;charset=ISO-8859-1;delsp=yes; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 9 Perhaps this should be advertised on the list. Thanks, Jean-Pierre Marquis Professeur agr=E9g=E9 D=E9partement de philosophie Universit=E9 de Montr=E9al C.P. 6128, succ. Centre-ville Montr=E9al Qc Canada H3C 3J7 t=E9l.: 514-343-2029 fax: 514-343-7899 D=E9but du message r=E9exp=E9di=E9 : > De: Grigori Mints > Date: 8 f=E9vrier 2006 21:44:58 GMT-05:00 > =C0: logic@cs.Stanford.EDU, logical-methods@lists.Stanford.EDU > Objet: Voevodsky > > See > http://math.stanford.edu/distinguished_voevodsky.htm > The first two lectures will be devoted to Homotopy lambda calculus. > > Abstract: > > Homotopy lambda calculus is a kind of dependent type system which =20 > comes together with a very natural semantics (models) with values in =20= > the homotopy category. I hope that it can be used to develop =20 > foundations of mathematics which are intuitive and at the same time =20= > formal enough to be implemented in proof checkers. I will start with a = =20 > brief introduction to the type systems for mathematicians. Then I will = =20 > describe the homotopy lambda calculus which is an instance of such =20 > systems and discuss how one can use it to formalize pure mathematics. > > The titles of the last two lectures will be announced later. > > > From rrosebru@mta.ca Thu Feb 9 21:46:40 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Feb 2006 21:46:40 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F7NHP-0001Jn-MW for categories-list@mta.ca; Thu, 09 Feb 2006 21:40:59 -0400 To: categories@mta.ca Subject: categories: Re: Question (fwd) Date: Thu, 09 Feb 2006 09:32:05 -0500 From: wlawvere@buffalo.edu Message-ID: <1139495525.43eb5265c8209@mail2.buffalo.edu> References: In-Reply-To: X-Mailer: University at Buffalo WebMail Cyrusoft SilkyMail v1.1.11 MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 10 Concerning Thomas Streicher's question about the internal linear functional (=distribution of compact support) monad on Froelicher's smooth category : see volume 1 of the journal Functional Analysis for two papers by Waelbroeck which show that the algebras are essentially determined by complete bornological spaces. Concerning Klaus Keimel's question about "abstract" compact convex sets, I do not recall a precise reference but is seems that Linton or Semadeni or both proved that they all do embed in locally convex linear spaces. This of course is in contrast with the noncompact finitary part of the probability theory, where there are those special algebras which are often discarded as spurious, but which in fact by a very natural adjoint to an algebraic functor record the face structure of any convex set as a semilattice. That raises the question: is there no equally natural way to record face structure for COMPACT convex sets ? Quoting Thomas Streicher : > My colleague Klaus Keimel has the following question and would be > glad > if someone could answer it. > If you want to answer him directly his e-mail address is > > keimel@mathematik.tu-darmstadt.de > > I have come across a different, but similar question concerning the > distribution monad on Froelicher spaces (as studied by Froelicher, > Kriegl > and Michor). Can one characterize elementarily the algebras for the > monad > T(X) = Lin(R^X,R) on \SS, the cartesian closed category of > Froelicher > spaces and "smooth" maps between them? I guess smooth and linear is > not > sufficient... > > Thomas Streicher > > > ----------------------------------------------------------------------- > The monad of probability measures over compact Hausdorf spaces > > If we assign to every compact Hausdorff space X the set PX of all > probability measures on X endowed with the vague (= weak*topology if > we consider PX embedded in the dual of C(X)), then we have a monad. > The unit e assign the Dirac measure to every point x in X, the > multiplication m assigns the barycentre of every probability measure > on PX. > > My question is: What are the algebras and the algebra homomorphisms > of this monad? > > It should be straightforward, that compact convex sets in locally > convex vector spaces are algebras. Probability measures on such > spaces > have a barycentre. Continuous affine maps should be homomorphisms. > > Are these all algebras and homomorphisms? > > One thinks that this should be known. Who knows about this? I would > be > interested in hints and in relevant references. > > Klaus Keimel > > > > From rrosebru@mta.ca Sat Feb 11 10:13:46 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 11 Feb 2006 10:13:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F7vMf-000672-6I for categories-list@mta.ca; Sat, 11 Feb 2006 10:04:41 -0400 Subject: categories: Glasgow PSSL: registration open From: Tom Leinster To: categories@mta.ca Content-Type: text/plain Date: Fri, 10 Feb 2006 17:36:26 +0000 Message-Id: <1139592986.19966.37.camel@tl-linux.maths.gla.ac.uk> Mime-Version: 1.0 Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 11 Dear All, You are warmly welcomed to the 83rd Peripatetic Seminar on Sheaves and Logic, to be held in Glasgow, Scotland, on 6-7 May. Everyone is invited to offer a talk, on any aspect of category theory and its applications. For information, see http://www.maths.gla.ac.uk/~tl/pssl/ If you just want to register, hit "reply" (not to the whole list!) and fill in the form below. Best wishes, Tom Leinster Richard Steiner +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Name: University or other affiliation: Would you like to give a talk? Title of talk: If you would like to submit an abstract, you are welcome to do so either now or later. Would you like a hotel room booked? Arrival date: Departure date: If you are not travelling alone, please specify how many people will be in your party and what type of room(s) you would like (single, twin or double). The provisional plan is to go to an Indian restaurant on Saturday night. (Glasgow has won Curry Capital of Britain.) Do you think you would like to come? If so, would you bring anyone else? +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ From rrosebru@mta.ca Sun Feb 12 19:28:54 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 12 Feb 2006 19:28:54 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F8QSR-0000Jz-OZ for categories-list@mta.ca; Sun, 12 Feb 2006 19:16:43 -0400 Date: Sat, 11 Feb 2006 15:41:42 +0000 From: ajp@inf.ed.ac.uk To: cmcs06@cs.nott.ac.uk Subject: categories: CMCS 06 Short Contributions final CFP MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;format="flowed" Content-Disposition: inline Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 12 This is the FINAL CALL for submissions to the Short Contributions section of CMCS 06, as advertised below. People are free to submit at any time; and if they need a prompt answer in order to apply for visas or accommodation or the like, please ask. ********************************************************************** CMCS 2006 8th International Workshop on Coalgebraic Methods in Computer Science http://conferences.inf.ed.ac.uk/cmcs06/cmcs06.html Vienna, Austria March 25-27, 2006 The workshop will be held in conjunction with the 9th European Joint Conferences on Theory and Practice of Software ETAPS 2006 March 25 - April 2, 2006 Aims and Scope During the last few years, it has become 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, Genova, Grenoble, Warsaw and Barcelona. The proceedings appeared as Electronic Notes in Theoretical Computer Science (ENTCS) Volumes 11,19, 33, 41, 65.1, 82.1 and 106. 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 those workshops ENTCS Location CMCS 2006 will be held in Vienna on March 25-27, 2006. It will be a satellite workshop of ETAPS 2006, the European Joint Conferences on Theory and Practice of Software. Programme Committee John Power (chair,Edinburgh), Luis Barbosa (Minho), Neil Ghani (Nottingham), H. Peter Gumm (Marburg), Marina Lenisa (Udine), Stefan Milius (Braunschweig), Larry Moss (Bloomington), Jan Rutten (Amsterdam), Hendrik Tews (Dresden), Tarmo Uustalu (Tallinn), Hiroshi Watanabe (Osaka). Keynote Speaker: Peter O'Hearn (Queen Mary, University of London) Invited Speakers: Corina Cirstea (University of Southampton) Alexander Kurz (University of Leicester) Submissions Two sorts of submissions will be possible this year: Papers to be evaluated by the programme committee for inclusion in the ENTCS proceedings: These papers must be written using ENTCS style files and be of length no greater than 20 pages. They must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. If a submission describes software, software tools, or their use, it should include all source code that is needed to reproduce the results but is not publicly available. If the additional material exceeds 5 MB, URL's of publicly available sites should be provided in the paper. Short contributions: These will not be published but will be compiled into a technical report of the University of Nottingham. They should be no more than two pages and may describe work in progress, summarise work submitted to a conference or workshop elsewhere, or in some other way appeal to the CMCS audience. Both sorts of submission should be submitted in postscript or pdf form as attachments to an email to cmcs06@cs.nott.ac.uk. The email should include the title, corresponding author, and, for the first kind of submission, a text-only one-page abstract. After the workshop, we expect to produce a journal proceedings of extended versions of selected papers to appear in Theoretical Computer Science. Important Dates Deadline for submission of regular papers: January 8, 2006. Notification of acceptance of regular papers: February 6, 2006. Final version for the preliminary proceedings: February 13, 2006. Deadline for submission of short contributions: February 28, 2006. Notification of acceptance of short contributions: March 6, 2006. For more information, please write to cmcs06@cs.nott.ac.uk. From rrosebru@mta.ca Tue Feb 14 20:28:25 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 14 Feb 2006 20:28:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F9ANH-0003EC-J5 for categories-list@mta.ca; Tue, 14 Feb 2006 20:18:27 -0400 From: Philippe Gaucher Reply-To: gaucher@pps.jussieu.fr To: categories@mta.ca Subject: categories: Bibliographical reference needed Date: Tue, 14 Feb 2006 12:52:32 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 13 Dear All, I would need please a bibliographical reference for the following fact : "Let C be a complete cocomplete cartesian closed category. Let I be a small category. Then the category of functors C^I is cartesian closed." (If Hom is the internal hom functor of C, let Hom(X_*,Y_*)=\int_i Hom(X_i,Y_i) ; then the internal hom of C^I is defined by HOM(X_*,Y_*)_j= j |-> Hom(X_* x 1[j], Y_*) where 1 is the terminal object of C and Z |-> Z[j] is left adjoint to the i-th evaluation functor X_* |-> X_j) Thanks in advance. pg. From rrosebru@mta.ca Tue Feb 14 20:28:25 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 14 Feb 2006 20:28:25 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F9AO2-0003HB-Di for categories-list@mta.ca; Tue, 14 Feb 2006 20:19:14 -0400 To: categories@mta.ca Subject: categories: Goedel Young Scholars' Competition - deadline 24 February, 2006 From: goedel2006@logic.at Date: Tue, 14 Feb 2006 14:28:23 +0100 Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 14 Call for Participation Young Scholars' Competition The Kurt G=F6del Centenary: Horizons of Truth organizers and sponsors invite young scholars in logic, mathematics, physics, philosophy, computer science and theology to submit project proposals for young scholars' competition honoring Kurt G=F6dels hundredth birthday. Web: http://www.logic.at/goedel2006/index.php?students Project Proposal Description Submitted project proposals should be strongly connected to the scientific achievements including recent applications and/or life of Kurt G=F6del. The proposals can cover any of the following disciplines: logic, mathematics, physics, computer science, theology or philosophy. Participation Criteria In order to participate in this competition, you must be born on or after January 1, 1970. Required documents 1.=09Project proposal 2.=09Curriculum vitae 3.=09List of bibliographic references Important note: Submissions should contain a description of the future research project, its relation to the fields of research as mentioned above, and to Kurt G=F6del's life or work, and possible applications. Including the list of references, and the CV it should not exceed six (6) pages in PDF format. Prizes Ten chosen projects will compete for three top prizes. 1st prize: 20 000 EUR 2nd and 3rd prize: 5000 EUR each Deadlines Submission deadline: Monday, 24. February 2006. 6 p.m. CET Notifications: Monday, 15. March 2006. Submissions For submission software and instructions, see: http://www.logic.at/goedel2006/index.php?submissions From rrosebru@mta.ca Wed Feb 15 17:41:12 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 15 Feb 2006 17:41:12 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F9UJ6-0000Gs-De for categories-list@mta.ca; Wed, 15 Feb 2006 17:35:28 -0400 Mime-Version: 1.0 (Apple Message framework v746.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Message-Id: <10983587-DA74-49E2-B737-9D8CA8BF4152@math.tulane.edu> Content-Transfer-Encoding: 7bit From: Michael Mislove Subject: categories: MFPS Final Call for Papers Date: Wed, 15 Feb 2006 15:15:53 -0600 To: categories@mta.ca Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 15 Dear Colleagues, This is a reminder that the deadline for submission to MFPS 22 is next Wednesday, February 22. The twenty-second conference on the Mathematical Foundations of Programming Semantics will take place in Genoa, Italy from May 24 through May 27, 2006. The invited speakers are: Marcelo Fiore, Cambridge Eugenio Moggi, Genova Prakash Panangaden, McGill Davide Sangiorgi, Bologna Peter Selinger, Dalhousie Steve Zdancewic, Penn In addition, we are planning three special sessions, one on Security, organized by Catherine Meadows (NRL), another on Real-time Systems, organized by Joel Ouaknine and James Worrell (Oxford), and one on Quantum Computing, organized by Michael Mislove, Prakash Panangaden and Peter Selinger. The remainder of the program will consist of paper submitted in response to this Call. Authors interested in submitting a paper for the meeting should submit an extended abstract of 15 pages or less to mfps@math.tulane.edu The submission should be in the form of a pdf file or PostScript file suitable for printing on a standard printing device. Authors of accepted papers will be notified by March 25. More details about the meeting, including the list of PC members, is available at the MFPS 22 home page http://www.math.tulane.edu/ ~mfps/mfps22,htm Best regards, Mike Mislove =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA =============================================== From rrosebru@mta.ca Fri Feb 17 11:21:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 17 Feb 2006 11:21:31 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FA7Ft-0006XZ-Nu for categories-list@mta.ca; Fri, 17 Feb 2006 11:10:45 -0400 Date: Thu, 16 Feb 2006 19:48:09 +0100 From: vigano@inf.ethz.ch To: categories@mta.ca Subject: categories: CFP: FCS-ARSPA'06 (Workshop on Foundations of Computer Security and Automated Reasoning for Security Protocol Analysis) Message-ID: <20060216184809.GA14114@inf.ethz.ch> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.4.1i Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 16 apologies for multiple copies ************************ **** **** **** FCS-ARSPA'06 **** **** **** ************************ A LICS'06 (and FLoC'06) Affiliated Workshop on FOUNDATIONS OF COMPUTER SECURITY and AUTOMATED REASONING FOR SECURITY PROTOCOL ANALYSIS Seattle, Washington, August 15-16, 2006 http://www.inf.ethz.ch/~vigano/fcs-arspa06 *********************** *** CALL FOR PAPERS *** *********************** Submission deadline: May 10, 2006 BACKGROUND, AIM AND SCOPE ========================= Computer security is an established field of computer science of both theoretical and practical significance. In recent years, there has been increasing interest in logic-based foundations for various methods in computer security, including the formal specification, analysis and design of security protocols and their applications, the formal definition of various aspects of security such as access control mechanisms, mobile code security and denial-of-service attacks, and the modeling of information flow and its application to confidentiality policies, system composition, and covert channel analysis. The workshop FCS-ARSPA'06 is the fusion of two workshops. The workshop FCS continues a tradition, initiated with the Workshops on Formal Methods and Security Protocols (FMSP) in 1998 and 1999, then with the Workshop on Formal Methods and Computer Security (FMCS) in 2000, and finally with the LICS satellite Workshop on Foundations of Computer Security (FCS) in 2002 through 2005, of bringing together formal methods and the security community. The ARSPA workshop is the third in a series of workshops on Automated Reasoning for Security Protocol Analysis, bringing together researchers and practitioners from both the security and the formal methods communities, from academia and industry, who are working on developing and applying automated reasoning techniques and tools for the formal specification and analysis of security protocols. The first two ARSPA workshops were held as satellite events of IJCAR'04 and of ICALP'05, respectively. The aim of the joint workshop FCS-ARSPA'06 is to provide a forum for continued activity in these areas, to bring computer security researchers in closer contact with the LICS community, and to give LICS attendees an opportunity to talk to experts in computer security. We thus solicit submissions of papers both on mature work and on work in progress. We are interested both in new results in theories of computer security and also in more exploratory presentations that examine open questions and raise fundamental concerns about existing theories, as well as in new results on developing and applying automated reasoning techniques and tools for the formal specification and analysis of security protocols. Possible topics include, but are not limited to: Automated reasoning techniques Access control and resource usage control Composition issues Authentication Formal specification Availability and denial of service Foundations of verification Covert channels Information flow analysis Confidentiality Language-based security Integrity and privacy Logic-based design for Intrusion detection Program transformation Malicious code Security models Mobile code Static analysis Mutual distrust Statistical methods Privacy Tools Security policies Trust management Security protocols All submissions will be peer-reviewed. Authors of accepted papers must guarantee that their paper will be presented at the workshop. SUBMISSION ========== Submissions should be at most 15 pages (a4paper, 11pt), including references, in the Springer LNCS style available at the URL http://www.springer.de/comp/lncs/authors.html The cover page should include title, names of authors, co-ordinates of the corresponding author, an abstract, and a list of keywords. It is recommended that submissions adhere to the specified format and length. Submissions that are clearly too long may be rejected immediately. Additional material intended for the referees but not for publication in the final version - for example details of proofs - may be placed in a clearly marked appendix that is not included in the page limit. Simultaneous submissions to a journal or another conference are accepted. Authors are invited to submit their papers electronically, as portable document format (pdf) or postscript (ps); please, do not send files formatted for work processing packages (e.g., Microsoft Word or Wordperfect files). The only mechanism for paper submissions is via the electronic submission web-site (which will soon be available). IMPORTANT DATES =============== Papers due: May 10, 2006 Notification of acceptance: June 16, 2006 Final paper versions due: July 14, 2006 Workshop: August 15-16, 2006 PUBLICATION =========== Informal proceedings will be made available in electronic format and they will be distributed to all participants of the workshop. The authors of the best papers might be invited to submit an extended revision for inclusion in a special issue of a journal, with an additional reviewing process. INVITED TALKS ============= To be announced PROGRAM COMMITTEE ================= * Alessandro Armando (Universita` di Genova, Italy) * Jorge R. Cuellar (SIEMENS AG, Munich, Germany) * Anupam Datta (Stanford University, USA) * Pierpaolo Degano (Universita` di Pisa, Italy; co-chair) * Pablo Giambiagi (Swedish Institute of Computer Science, Sweden) * Virgil Gligor (University of Maryland, USA) * Roberto Gorrieri (Universita` di Bologna, Italy) * Carl A. Gunter (University of Illinois at Urbana-Champaign, USA) * Joshua Guttman (Mitre, USA) * Ralf Kuesters (Christian-Albrechts-Universitaet zu Kiel, Germany; co-chair) * Ninghui Li (Purdue University, USA) * Sjouke Mauw (University of Eindhoven, The Netherlands) * Peter Ryan (University of Newcastle, UK) * Luca Vigano` (ETH Zurich, Switzerland; co-chair) * Laurent Vigneron (INRIA-LORRAINE, Nancy, France) * Bogdan Warinschi (INRIA-LORRAINE, Nancy, France) * Steve Zdancewic (University of Pennsylvania, USA; co-chair) FCS Steering Committee: * Martin Abadi (University of California at Santa Cruz, USA) * Joshua Guttman (MITRE, USA) * John Mitchell (Stanford University, USA) * Andrei Sabelfeld (Chalmers, Sweden; chair) * Andre Scedrov (University of Pennsylvania, USA) ADDITIONAL INFORMATION ====================== Information about registration, travel, and venue can be found at the LICS'06 and FLoC'06 web-sites. For further information send an email to the workshop co-chairs at fcs-arspa06 -at- lists.inf.ethz.ch From rrosebru@mta.ca Sun Feb 19 11:34:39 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 19 Feb 2006 11:34:39 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FAqLH-0005Kf-By for categories-list@mta.ca; Sun, 19 Feb 2006 11:19:19 -0400 Subject: categories: CT2006: deadlines and Mac Lane, Eilenberg special session To: categories@mta.ca (Categories List) Date: Sun, 19 Feb 2006 09:33:53 -0400 (AST) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: <20060219133353.894CF1084A@sigma.mathstat.dal.ca> From: selinger@mathstat.dal.ca (Peter Selinger) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 17 ANNOUNCEMENT OF SPECIAL SESSION IN HONOR OF THE WORKS OF MAC LANE AND EILENBERG and REMINDER OF UPCOMING DEADLINES International Category Theory Conference CT 2006 June 25 - July 1, 2006 White Point, Nova Scotia http://www.mathstat.dal.ca/~selinger/ct2006/ * * * SPECIAL SESSION ON THE WORKS OF MAC LANE AND EILENBERG ------------------------------------------------------ A special commemorative session in honor of the two founders of category theory, Saunders Mac Lane and Samuel Eilenberg, will be held at CT 2006. Contributors who are interested in having their talk be part of this special session should indicate so when they submit their abstract. Since the special session will be one-half day, only a limited number of talks can be accommodated. UPCOMING DEADLINES: ------------------- February 27: Submission of Abstracts ------------ Prospective speakers should submit an abstract of up to one page. Abstracts should be sufficiently detailed to allow the scientific committee to assess the merits of the work. Submissions should be in plain text, Postscript, or PDF format, and must be sent to ct06@mathstat.dal.ca by FEBRUARY 27. (Proposals for talks at the special session on Mac Lane and Eilenberg will be accepted until March 15). Receipt of all submissions will be acknowledged by return email. Authors will be notified by March 30 of the acceptance of their talks. March 1: Early (=cheaper) Registration -------- This is a reminder that participants have to register by MARCH 1 to take advantage of the cheaper rate of $120 (regular) or $75 (reduced). After March 1, the registration fees will increase to $150 (regular) and $100 (reduced). So please register now at: https://sigma.mathstat.dal.ca/~selinger/ct2006/registration.php In case someone needs to cancel their registration, it will be possible to do so (for a full refund of the registration fee) until April 20. We also recommend that you book your rooms at Whitepoint as soon as possible. See the CT 2006 website for details. * * * (The remainder of this announcement contains information repeated from previous announcements.) The International Category Theory Conference (CT) covers all areas of pure and applied category theory. Topics of interest include, but are not limited to: higher dimensional categories, categorical logic, applications of categories in algebra, topology, combinatorics, and other areas of mathematics, applications of category theory to computer science, physics and other mathematical sciences. Previous meetings in this series were held in Vancouver (2004), Como (2000), Coimbra (1999), Vancouver (1997), Halifax (1995), Tours (1994), Isle of Thorns (1992), Montreal (1991), and Como (1990). CT 2006 will be held at White Point Beach Resort (http://www.whitepoint.com/), a seaside resort in Nova Scotia (Canada), about 100 minutes' drive from Halifax. It will be an active research-oriented conference, in something of an "Oberwolfach style". All those interested in category theory and its applications are welcome. INVITED SPEAKERS: (updated) Invited lectures will be given by: Kathryn Hess (EPF Lausanne) Steve Lack (University of Western Sydney) Tom Leinster (University of Glasgow) Steve Schanuel (SUNY Buffalo) Peter Selinger (Dalhousie University) REGISTRATION: The registration fees for CT 2006 are as follows: If registering by March 1 (early registration): Regular -- $120 Reduced (*) -- $75 If registering after March 1 (late registration): Regular -- $150 Reduced (*) -- $100 (*) the reduced registration fee applies to students, postdocs, and researchers without grant. Please register at: https://sigma.mathstat.dal.ca/~selinger/ct2006/registration.php ACCOMMODATIONS, ARRIVAL, DEPARTURE: Please book your rooms at White Point Beach Resort as soon as possible. We encourage all participants to book this by the end of January; keep in mind that it can be canceled later for a $5 fee. The normal arrival date is Sunday, June 25, and the normal departure date is Saturday, July 1. There will be an informal opening reception / buffet dinner on June 25 from 6:30-10:30pm. The normal check-in time is 2pm and check-out time is 11am. If you need to make special arrangements for early arrival or late departure, please make them by contacting White Point directly. The conference venue offers a choice of accommodation, both in comfortable finished cabins and in "hotel-style" rooms. All meals are included in the price of the rooms. Subject to availability, White Point Beach Resort has agreed to extend the conference rates to the weeks before and after the conference in case any guests wish to stay longer. If you would like to arrange this, please contact White Point directly. For reservations, please contact White Point Beach Resort: Tel: 1-800-565-5068 (U.S. and Canada) Tel: +1-902-354-2711 (international) Fax: +1-902-354-7278 Email reservations: greatday@whitepoint.com AIRPORT TRANSPORTATION: We will arrange for shared transportation between Halifax International Airport and White Point Beach Resort on the days of arrival and departure, at no extra charge to conference participants and their guests. To take advantage of this, please let us know, at ct06@mathstat.dal.ca, your arrival and departure times, airline, and flight numbers, as soon as you have this information. Please note that White Point Beach Resort is 100 minutes driving distance from the airport, and there is no convenient alternative transportation available except for renting a car. IMPORTANT DEADLINES: Jan 25, 2006: early booking of rooms Feb 15, 2006: application for graduate student support Feb 27, 2006: submission of abstracts Mar 1, 2006: early registration Mar 15, 2006: proposals for special session talks Mar 30, 2006: notification of authors Apr 20, 2006: booking of rooms Apr 20, 2006: cancellation of registrations SCIENTIFIC COMMITTEE: Jiri Adamek John Baez Michael Barr Eugenia Cheng Maria Manuel Clementino Marcelo Fiore Peter Freyd Jonathon Funk Peter Johnstone Steve Lack Susan Niefield Phil Scott Ross Street Walter Tholen (chair) Enrico Vitale ORGANIZERS: Robert Dawson (rdawson@cs.stmarys.ca) Dorette Pronk (pronk@mathstat.dal.ca) Peter Selinger (selinger@mathstat.dal.ca) CONFERENCE EMAIL AND WEBSITE: ct06@mathstat.dal.ca http://www.mathstat.dal.ca/~selinger/ct2006/ From rrosebru@mta.ca Wed Feb 22 17:00:46 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 22 Feb 2006 17:00:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FC0w0-0006XG-0X for categories-list@mta.ca; Wed, 22 Feb 2006 16:50:04 -0400 Message-ID: <20060221173458.3c35kr942s4c4swc@mail.math.yorku.ca> Date: Tue, 21 Feb 2006 17:34:58 -0500 From: tholen@mathstat.yorku.ca To: categories@mta.ca Subject: categories: Special Session Mac Lane/Eilenberg MIME-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;format="flowed" Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.4) Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 18 Further to the announcement by the Organizing Committee of CT06, I am happy to report that Bill Lawvere has agreed to organize and chair the "Special Session in Honour of the Works of Mac Lane and Eilenberg" at the meeting. Walter Tholen. From rrosebru@mta.ca Wed Feb 22 17:05:11 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 22 Feb 2006 17:05:11 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FC19d-0007Hs-OU for categories-list@mta.ca; Wed, 22 Feb 2006 17:04:09 -0400 Date: Wed, 22 Feb 2006 10:08:01 +0100 (MET) From: Patrik Eklund To: categories@mta.ca Subject: categories: Virtual classrooms and Cat Th Education Message-ID: 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: 19 Dear Friends and Colleagues! I will be speaking categories and categorical education but let me begin with technology. We have been using virtual classrooms now for quite a while. It's useful for courses at all level, distant supervision can be carried out, etc. You can even do research collaboration in this way. Many already do, with different ambitions concerning technology and content. I am sure that I am not aware of on-going processes, and if any reader already has gone far beyond this, please stop reading and accept my apology for this spam mail. I am not speaking NetMeeting or Skype where you only have audio and video transmission. We are using Marratech where you have whiteboards and shared applications. In particular, the whiteboard is very useful as you can have many of them at the same time, and what is next best, you can save the whiteboard files and use/update them online before and after meetings, i.e. you can prepare your agenda/slides and the whiteboard prior to coming together in the virtual classroom. The best thing is that the Marratech client is free of charge. The server is rather costly but we have one in Umea and I would like to make this available for Virtual Cat Th Education. Basic and Advanced courses in category theory both for mathematicians, but also, as in my case, for computer scientists. I came to this idea now when I am trying to recruit interest in my own department for these topics. E.g. I want to do some basic things with categories, functors, and natural transformations. From there monads are rather close by. Further, I want to teach topoi/toposes and also say some words on \lambda-calculi. Universal algebra, categorically, is a further priority. Etc etc. *** Anybody out there sharing these ideas? Can we develop something together? The problem often being that each and every site may come up with 4-7 students, but combining 4-5 sites gives a nice classroom. And, of course, teaching can be shared. Joint lecture notes would be important, I believe. Etc etc. Drop me a message if you are interested in developing these ideas further. Cheers, Patrik peklund@cs.umu.se +46 70 5864414 From rrosebru@mta.ca Thu Feb 23 13:47:11 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 23 Feb 2006 13:47:11 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FCKSy-0002xV-Fw for categories-list@mta.ca; Thu, 23 Feb 2006 13:41:24 -0400 Subject: categories: Voevodsky on the homotopy lambda calculus To: categories@mta.ca (categories) Date: Wed, 22 Feb 2006 13:53:01 -0800 (PST) From: "John Baez" X-Mailer: ELM [version 2.5 PL6] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 20 As has already been pointed out here, Vladimir Voevodsky is giving lectures at Stanford on the "homotopy lambda calculus": http://math.stanford.edu/distinguished_voevodsky.htm Can anyone report on what he said? Phil Scott has been teaching me about the lambda calculus and related stuff. He noted that in getting a cartesian closed category from intuitionistic logic, one takes sequents Gamma |- Delta as objects and *equivalence classes* of proofs as morphisms. One needs to take equivalence classes to get composition of morphisms to be associative, etc. From an n-categorical viewpoint it's natural to avoid working with equivalence classes and instead use 2-morphisms between morphisms, like associators, and so on, thus getting a "weak cartesian closed omega-category" - a concept which, alas, has probably not been defined yet. For someone like Voevodsky it would be natural to use ideas from homotopy theory instead and define something like a "cartesian closed category up to coherent homotopy". Such a thing should be lurking in the ordinary typed lambda calculus. Is this what Voevodsky is talking about? Or...? Best, jb From rrosebru@mta.ca Fri Feb 24 19:56:34 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Feb 2006 19:56:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FCmfB-0000IE-Vo for categories-list@mta.ca; Fri, 24 Feb 2006 19:47:54 -0400 Message-ID: <43FE2779.2050106@cs.nott.ac.uk> Date: Thu, 23 Feb 2006 21:22:01 +0000 From: Conor McBride User-Agent: Mozilla Thunderbird 1.0.2 (Macintosh/20050317) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CFP: Mathematically Structured Functional Programming Content-Type: text/plain; charset=3DISO-8859-1; format=3Dflowed Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 21 CALL FOR PAPERS Workshop on Mathematically Structured Functional Programming MSFP 2006 Kuressaare, Estonia, 2 July 2006 http://cs.ioc.ee/mpc-amast06/msfp/ a satellite workshop of MPC 2006 a "small workshop" of the TYPES project Background Something wonderful happened when monads arrived in Haskell: some human mathematics explaining the structure of certain computational phenomena became a mechanical means to implement those phenomena. It's a good way to go about functional programming - to dig out the mathematical structure underlying a problem and set it to work! There's more where monads came from, and we want it. This new workshop is about getting it. In recent years, a diverse array of mathematical structures has appeared in our programs: monads dualise to comonads and generalise to Freyd categories aka 'arrows'; 'container' types have a generalised polynomial structure supporting generic programming, not to mention a differential calculus; isomorphisms from 'high school algebra' are used to search libraries and repair type errors; coalgebras give structure to recursion; the list goes on... MSFP is broad in scope, covering the extraction of functionality from structure wherever it can be found. It complements the remit of its host conference, Mathematics of Program Construction, by seeking to enrich the language and toolset available for specifications and programs alike. It is also a "small workshop" of the FP6 IST coordination action TYPES. Invited speakers Andrzej Filinski, K=F8benhavns Universitet John Power, University of Edinburgh Important dates * Submission of papers: 10 April 2006 * Notification of authors: 8 May 2006 * Camera-ready version: 5 June 2006 Topics Submissions are welcome on, but by no means restricted to, topics from the following partially computed coinductive list: * structured effectful computation * structured recursion * structured tree and graph operations * structured syntax with variable binding * structures for datatype-genericity * structures for search * structured representations of functions * structured manipulation of mathematical structure * structured in functional programming Authors concerned about the suitability of a topic are very welcome to contact Conor McBride, ctm(at)cs.nott.ac.uk. Submission and publication Papers in pdf not exceeding 15 pages and adhering to the eWiC style must be submitted by 10 April 2006 via an online submission webpage. Papers must report previously unpublished work and not be submitted concurrently to another conference with refereed proceedings. Accepted papers must be presented at the workshop by one of the authors. The proceedings of MSFP 2006 will be published in the Electronic Workshops in Computing (eWiC) series of the British Computer Society, http://ewic.bcs.org/. After the workshop, the authors of the best papers will be invited to submit revised and expanded versions to a special issue of the Journal of Functional Programming from Cambridge University Press. Programme committee Yves Bertot, INRIA Sophia Antipolis Marcelo Fiore, University of Cambridge Masahito Hasegawa, Kyoto University Graham Hutton, University of Nottingham Paul Levy, University of Birmingham Andres L=F6h, Universitt Bonn Christoph L=FCth, Universitt Bremen Conor McBride, University of Nottingham (co-chair) Marino Miculan, Universit=E0 degli Studi di Udine Randy Pollack, University of Edinburgh Amr Sabry, Indiana University Tarmo Uustalu, Institute of Cybernetics (co-chair) Main conferences MSFP 2006 is a satellite workshop of the 8th International Conference on Mathematics on Program Construction, MPC 2006, to take place 3-5 July. Co-located with MPC 2006, the 11th International Conference on Algebraic Methodology and Software Technology, AMAST 2006, will follow 5-8 July. Venue Kuressaare (pop. 16000) is the main town on Saaremaa, the second-largest island of the Baltic Sea. Kuressaare is a charming seaside resort on the shores of the Gulf of Riga highly popular with Estonians as well as visitors to Estonia. The scientific sessions of MPC/AMAST 2006 will take place at Saaremaa Spa Hotel Meri, one among the several new spa hotels in the town. The social events will involve a number of sites, including the 14th-century episcopal castle. Accommodation will be at Saaremaa Spa Hotels Meri and R=FC=FCtli. To get to Kuressaare and away, one must pass through Tallinn (pop. 402000), Estonia's capital city. Tallinn is famous for its picturesque medieval Old Town, inscribed on UNESCO's World Heritage List. TYPES support MSFP 2006 is an official workshop of the EU FP6 IST coordination action TYPES. Participants from TYPES sites/subsites may use project funds to cover their travel and participation. Local organizers MPC/AMAST 2006 is organized by Institute of Cybernetics, a research institute of Tallinn University of Technology. The local organizers are Tarmo Uustalu (chair), Monika Perkmann, Juhan Ernits, Ando Saabas, Olha Shkaravska, Kristi Uustalu. Contact email address of the local organizers: mpc06(at)cs.ioc.ee. From rrosebru@mta.ca Fri Feb 24 19:56:34 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Feb 2006 19:56:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FCmgV-0000LZ-Jo for categories-list@mta.ca; Fri, 24 Feb 2006 19:49:15 -0400 From: Andrej Bauer To: categories Date: Thu, 23 Feb 2006 23:24:49 +0100 User-Agent: KMail/1.8.3 References: MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit Content-Disposition: inline Message-Id: <200602232324.50115.Andrej.Bauer@andrej.com> Subject: categories: Re: Voevodsky on the homotopy lambda calculus Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 22 On Wednesday 22 February 2006 22:53, John Baez wrote: > From an n-categorical > viewpoint it's natural to avoid working with equivalence classes > and instead use 2-morphisms between morphisms, like associators, > and so on, thus getting a "weak cartesian closed omega-category" - > a concept which, alas, has probably not been defined yet. I don't know about the omega-wheel, but at least the 2-wheel needs not be reinvented. For "cartesian closed 2-categories", a relevant reference is R.A.G. Seely, "Modelling computations: A 2-categorical framework". In Proceedings of the Second Symposium on Logic in Computer Science, pages 61--71, IEEE Computer Science Press, June 1987. I believe the above paper is "the first" on this topic (am I wrong?), and there must be more recent work. I know Neil Ghani did some, but Google also knows about "2-Lambda Calculus" by David Rydeheard, see http://www.cs.man.ac.uk/~david/publications/TwoLambdaCalculus.ps . Andrej From rrosebru@mta.ca Fri Feb 24 19:56:34 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Feb 2006 19:56:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FCmiB-0000QP-EU for categories-list@mta.ca; Fri, 24 Feb 2006 19:50:59 -0400 Date: Fri, 24 Feb 2006 11:04:49 +0100 From: "Urs Schreiber" To: categories Subject: categories: multicategory algebras MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 23 Dirk Kreimer and Alain Connes have developed a Hopf algebraic description of the process of renormalization in quantum field theory. Their starting point is the definition of a certain algebra structure on the space of all (Feynman-)graphs. The definition can be found, for instance, in equation (6) of http://arxiv.org/abs/hep-th/0510202 . I suspect that this algebra is most elegantly expressed as the "multicategory algebra" of the obvious multicategory of (Feynman-)graphs. This multicategory should be the obvious slight generalization of example 4.2.14 in Tom Leinster's book http://arxiv.org/abs/math.CT/0305049 . Here by "multicategory algebra" I mean a generalization to multicategories of the concept "category algebra" or "path algebra" of an ordinary category. I.e. the algebra generated by the morphisms in the category with the product derived from the composition law in the category. (Hence, in particular I am *not* referring to the concept "algebra *for* a multicategory" as in "algebra for an operad", discussed in section 4.3 of Leinster's book.) I would think such a concept of a multicategory(-path-)algebra should exist and should be given by the obvious generalization of formula (6) in the above cited paper. This concept seems to be so natural that I expect it must have been considered before. If so, could anyone point me to relevant sources? From rrosebru@mta.ca Fri Feb 24 19:56:34 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Feb 2006 19:56:34 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FCmil-0000R1-Kg for categories-list@mta.ca; Fri, 24 Feb 2006 19:51:35 -0400 Message-ID: <43FF74EB.6020109@cs.stmarys.ca> Date: Fri, 24 Feb 2006 17:04:43 -0400 From: "Robert J. MacG. Dawson" User-Agent: Mozilla Thunderbird 1.0.2 (Windows/20050317) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CT06: Deadlines approaching! Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 24 To all planning to attend CT06: Please note that the general deadline for abstracts, February 27th, is almost here. There appears to be a significant number of people intending to speak who have not yet submitted their abstracts. Legitimate submissions for the Eilenberg-Mac Lane commemorative session are welcome up to March 15th. However, we would ask people wishing to talk on a topic without particularly strong "Eilenberg-Mac Lane" connections (and category theory has taken many new directions since the heyday of our founders) not to use this as an excuse for late submission; it is not fair to the hard-worked scientific committee. Also, while the list of participants who have already booked at White Point has gratifyingly many familiar names (thank you!), we have noted that many who we expect to see in June have _not_ yet booked. The management at White Point may not be as used as we are to the categorical habit of leaving these things till the last minute, and are starting to get a little concerned, wondering if they will have to release some of the rooms in our block booking to the general public. Remember, the earlier you book, the better the choice of rooms/cabins; this will be especially true if White Point do have to release some units, when the choice available may drop sharply. With apologies, The Organizing Committee From rrosebru@mta.ca Sun Feb 26 11:27:27 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 26 Feb 2006 11:27:27 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDNe6-0006yK-RX for categories-list@mta.ca; Sun, 26 Feb 2006 11:17:14 -0400 Date: Sun, 26 Feb 2006 12:38:27 +0000 (GMT) From: Paul B Levy To: categories Subject: categories: Re: Voevodsky on the homotopy lambda calculus In-Reply-To: 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: 25 > Phil Scott has been teaching me about the lambda calculus > and related stuff. He noted that in getting a cartesian > closed category from intuitionistic logic, At the risk of boring people by repeating a point I've made on this list before: a model of intuitionistic logic is a *bi*cartesian closed category. I see no reason to regard disjunction as more "peripheral" to intuitionistic logic than implication. (And, likewise, no reason to regard sum types as more peripheral to simple type theory than function types.) Does anybody disagree? Ccc's without coproducts (e.g. domains and continuous maps) arise in the study of call-by-name languages with effects (e.g. divergence). But they are not models of intuitionistic logic. I appreciate that all John said was that a model constructed from syntax is a ccc, which is true because it's a bi-ccc, so he didn't actually contradict this point. Paul From rrosebru@mta.ca Sun Feb 26 22:11:13 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 26 Feb 2006 22:11:13 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDXlX-00065e-CO for categories-list@mta.ca; Sun, 26 Feb 2006 22:05:35 -0400 Date: Sun, 26 Feb 2006 11:18:45 -0500 (EST) From: Peter Freyd Message-Id: <200602261618.k1QGIjNW003204@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: intuitionism and disjunction Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 26 Paul Levy writes ...a model of intuitionistic logic is a *bi*cartesian closed category. I see no reason to regard disjunction as more "peripheral" to intuitionistic logic than implication. (And, likewise, no reason to regard sum types as more peripheral to simple type theory than function types.) Does anybody disagree? The original intuitionists did, of course, see such reasons. But for those who don't care about such issues as the nature of mathematical existence there's this reason: if by a *bi*cartesian closed category one were to mean a ccc category whose dual is also ccc then one would be stuck with that fact that all *bi*cartesian closed categories are just pre-ordered sets. The status of disjunction and sum types in the presence of function types is, indeed, significantly different from the status of conjunction and products types. Let me take the occasion to record a factoid I don't think I ever had an excuse to record before (and don't really have one now). Define the notion of a Heyting semi-lattice (HSL) by removing disjunction and bottom from the definition of Heyting algebra. Define a _linear_ HSL as one that satisfies the further equation ((x -> y) -> z) ^ ((y -> x) -> z) = z e.g. any linearly ordered set with top (indeed, every linear HSL is representable as a sub HSL of a product of linear ones). In a linear HSL one may construct disjunction as ((x -> y) -> y) ^ ((y -> x) -> x) The factoid of interest is this sort-of converse: the only HSL varieties in which every member is a lattice are varieties of linear HSLs. From rrosebru@mta.ca Mon Feb 27 09:33:16 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 09:33:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDiTd-0005m2-Lc for categories-list@mta.ca; Mon, 27 Feb 2006 09:31:49 -0400 Message-ID: <4402EE6D.8070607@cs.unibo.it> Date: Mon, 27 Feb 2006 13:19:57 +0100 From: Mario Bravetti User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: WS-FM 2006 Call For Papers Content-Type: text/plain; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 27 3rd International Workshop on Web Services and Formal Methods (WS-FM 2006) 8-9 September 2006, Vienna, Austria http://cs.unibo.it/ws-fm06 Official event of "The Process Modelling Group" http://www.process-modelling-group.org Co-located with BPM 2006 4th International Conference on Business Process Management http://bpm2006.tuwien.ac.at SCOPE Web Services technology aims at providing standard mechanisms for describing the interface and the services available on the web, as well as protocols for locating such services and invoking them (e.g. WSDL, UDDI, SOAP). Innovations are mainly devoted to the definition of standards that support the specification of complex services out of simpler ones (the so called Web Service orchestration and choreography). Several proposals have been already set up: BPML, XLANG and BizTalk, WSFL, WS-BPEL, WS-CDL, etc... Formal methods, which provide formal machinery for representing and analysing the behavior of communicating concurrent/distributed systems, are playing a fundamental role in the development of such innovations. First of all they are exploited to understand the basic mechanisms (in terms of semantics) which characterize different orchestration and choreography languages and to focus on the essence of new features that are needed. Secondly they provide a formal basis for reasoning about Web Service semantics (behaviour and equivalence): e.g. for realizing registry services where retrieval is based on the meaning and behaviour of a service and not just a Web Service name. Thirdly, the studies on formal coordination paradigms can be exploited for developing mechanisms for complex run-time Web Service coordination. Finally, given the importance of critical application areas for Web Services like E-commerce, the development of the Web Service technology can certainly take advantage from formal analisys of security properties and performance in concurrency theory. The aim of the workshop is to bring together researchers working on Web Services and Formal Methods in order to facilitate fruitful collaboration in this direction of research. This, potentially, could also have a great impact on the current standardization phase of Web Service technologies. LIST OF TOPICS The topics of interest include, but are not limited to: - Protocols and standards for WS (SOAP, WSDL, UDDI, etc... ) - Languages and description methodologies for Coreography/Orchestration/Workflow (BPML, XLANG and BizTalk, WSFL, WS-BPEL, WS-CDL, YAWL, etc... ) - Coordination techniques for WS (transactions, agreement, coordination services, etc...) - Semantics-based dynamic WS discovery services (based on Semantic Web/Ontology techniques or other semantic theories) - Security, Performance Evaluation and Quality of Service of WS - Semi-structured data and XML related technologies SUBMISSIONS Submissions must be original and should not have been published previously or be under consideration for publication while being evaluated for this workshop. We encourage also the submission of tool papers, describing tools based on formal methods, to be exploited in the context of Web Services applications. Papers are to be prepared in LNCS format and must not exceed 15 pages. Accepted papers will be published in the workshop proceedings as a volume of Lecture Notes in Computer Science (LNCS). As done for previous editions of the workshop, we intend to publish a journal special issue inviting full versions of papers selected among those presented at the workshop. IMPORTANT DATES April 21, 2006: Submission deadline June 6, 2006: Notification of acceptance June 20, 2006: Camera ready September 8-9, 2006: Workshop dates PROGRAM COMMITTEE Co-Chairs Mario Bravetti University of Bologna, Italy Gianluigi Zavattaro University of Bologna, Italy Board of "The Process Modelling Group" Wil van der Aalst Eindhoven Univ.of Technology, The Netherlands Rob van Glabbeek NICTA, Sydney, Australia Keith Harrison-Broninski Role Modellers Ltd. Robin Milner Cambridge University, UK Roger Whitehead Office Futures Other PC members Marco Aiello University of Trento, Italy Farhad Arbab CWI, The Netherlands Matteo Baldoni University of Torino, Italy Jean-Pierre Banatre University of Rennes1 and INRIA, France Boualem Benatallah University of New South Wales, Australia Karthik Bhargavan Microsoft research Cambridge, UK Roberto Bruni University of Pisa, Italy Michael Butler University of Southampton, UK Fabio Casati HP Labs, USA Rocco De Nicola University of Florence, Italy Marlon Dumas Queensland University of Technology, Australia Schahram Dustdar Wien University of Technology, Austria Gianluigi Ferrari University of Pisa, Italy Jose Luiz Fiadeiro University of Leicester, UK Stefania Gnesi CNR Pisa, Italy Reiko Heckel University of Leicester, UK Kohei Honda Queen Mary, University of London, UK Nickolas Kavantzas Oracle Co., USA Leila Kloul Universit=E9 de Versailles, France Cosimo Laneve University of Bologna, Italy Mark Little JBoss Inc Natalia L=F3pez University Complutense of Madrid, Spain Roberto Lucchi University of Bologna, Italy Jeff Magee Imperial College London, UK Fabio Martinelli CNR Pisa, Italy Manuel Mazzara University of Bolzano, Italy Ugo Montanari University of Pisa, Italy Shin Nakajima National Institute of Informatics and JST, Japan Manuel Nunez University Complutense of Madrid, Spain Fernando Pelayo University of Castilla-La Mancha, Albacete,Spain Marco Pistore University of Trento, Italy Wolfgang Reisig Humboldt University, Berlin, Germany Vladimiro Sassone University of Southampton, UK Marjan Sirjani Tehran University, Iran Friedrich Vogt Technical University of Hamburg-Harburg, Germany Martin Wirsing Ludwig-Maximilians University Munchen, Germany From rrosebru@mta.ca Mon Feb 27 09:33:16 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 09:33:16 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDiRU-0005b7-0X for categories-list@mta.ca; Mon, 27 Feb 2006 09:29:36 -0400 Date: Mon, 27 Feb 2006 03:00:04 +0000 (GMT) From: Paul B Levy To: categories@mta.ca Subject: categories: Re: intuitionism and disjunction In-Reply-To: <200602261618.k1QGIjNW003204@saul.cis.upenn.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: 28 Dear Peter. > I see no reason to regard disjunction as more "peripheral" to > intuitionistic logic than implication. (And, likewise, no reason to > regard sum types as more peripheral to simple type theory than function > types.) Does anybody disagree? > > The original intuitionists did, of course, see such reasons. But for > those who don't care about such issues as the nature of mathematical > existence Can you explain the "of course" here, please? What were these reasons, and do they still hold water? I would have thought that tuples pose less of an ontological difficulty than functions. > there's this reason: if by a *bi*cartesian closed category one were to > mean a ccc category whose dual is also ccc What I meant was cartesian closed category with finite coproducts. > then one would be stuck with that fact that all *bi*cartesian closed > categories are just pre-ordered sets. > > The status of disjunction and sum types in the presence of function > types is, indeed, significantly different from the status of > conjunction and products types. I don't know what you mean - maybe that product types are more similar to function types than sum types are? If so, I agree, but I was comparing function types with sum types, not (function and sum) with (function and product). Paul From rrosebru@mta.ca Mon Feb 27 09:34:00 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 09:34:00 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDiV8-0005uK-4c for categories-list@mta.ca; Mon, 27 Feb 2006 09:33:22 -0400 Date: Mon, 27 Feb 2006 08:26:37 -0500 (EST) From: Peter Freyd Message-Id: <200602271326.k1RDQb3K008051@saul.cis.upenn.edu> To: categories@mta.ca Subject: categories: Re: intuitionism and disjunction Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 29 Paul Levy asks how the original intuitionists viewed disjunction. I don't know how to say it better than this paragraph from Wikipedia (anyone know who wrote it?). The disjunction and existence properties are validated by intuitionistic logic and invalid for classical logic; they are key criteria used in assessing whether a logic is constructive.... The disjunction property is a finitary analogue, in an evident sense. Namely given two or finitely many propositions P_i, whose disjunction is true, we want to have an explicit value of the index i such that we have a proof of that particular P_i. There are quite concrete examples in number theory where this has a major effect. It is a (meta)theorem that in free Heyting algebras and free topoi (and all sorts of variations thereon) that the disjunction property holds. In the free topos that translates to the statement that the terminator, 1, is not the join of two proper subobjects. Together with the existence property it translates to the assertion that 1 is an indecomposable projective object -- the functor it represents (i.e. the global-section functor) preserves epis and coproducts. (And with a little more work one can show it also preserves co-equalizers.) From rrosebru@mta.ca Mon Feb 27 19:30:38 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 19:30:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDriX-0000NH-T4 for categories-list@mta.ca; Mon, 27 Feb 2006 19:23:49 -0400 Message-ID: <440335A6.3050806@cs.stanford.edu> Date: Mon, 27 Feb 2006 09:23:50 -0800 From: Vaughan Pratt Reply-To: pratt@cs.stanford.edu Organization: Stanford University User-Agent: Mozilla Thunderbird 0.9 (Windows/20041103) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories list Subject: categories: Undirected graphs citation Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 30 What would be an early reference for the representation of undirected graphs (of the set-enriched rather than {0,1}-enriched kind) as presheaves on the full subcategory 1 and 2 of Set? Vaughan Pratt From rrosebru@mta.ca Mon Feb 27 19:30:38 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 19:30:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDrj5-0000PE-C8 for categories-list@mta.ca; Mon, 27 Feb 2006 19:24:23 -0400 Date: Mon, 27 Feb 2006 11:07:28 -0800 From: Toby Bartels To: categories@mta.ca Subject: categories: Re: intuitionism and disjunction Message-ID: <20060227190727.GA23248@math-rs-n03.ucr.edu> References: <200602271326.k1RDQb3K008051@saul.cis.upenn.edu> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 31 Peter Freyd wrote: >Paul Levy asks how the original intuitionists viewed disjunction. I >don't know how to say it better than this paragraph from Wikipedia >(anyone know who wrote it?). >From the editing history : it looks like the part before the ellipsis was written by English Wikipedia User Chalst , who is apparently Charles Stewart, a postdoc at the International Centre for Computational Logic; and the rest was written by English Wikipedia User Charles Matthews , who is now a hobbyist but was once an academic mathematician. (I'm familiar with Charles Matthews and trust him, if my opinion matters to anybody; I don't know Chalst.) Of course, either may have copied from somewhere else without proper attribution (that's been common ~within~ Wikipedia --that is copying or moving from one WP article to another-- but it's pretty rare ~into~ Wikipedia, in my experience.) > The disjunction and existence properties are validated by > intuitionistic logic and invalid for classical logic; they are key > criteria used in assessing whether a logic is constructive.... The > disjunction property is a finitary analogue, in an evident sense. > Namely given two or finitely many propositions P_i, whose > disjunction is true, we want to have an explicit value of the index > i such that we have a proof of that particular P_i. There are quite > concrete examples in number theory where this has a major effect. >It is a (meta)theorem that in free Heyting algebras and free topoi >(and all sorts of variations thereon) that the disjunction property >holds. In the free topos that translates to the statement that the >terminator, 1, is not the join of two proper subobjects. Together with >the existence property it translates to the assertion that 1 is an >indecomposable projective object -- the functor it represents (i.e. >the global-section functor) preserves epis and coproducts. (And with >a little more work one can show it also preserves co-equalizers.) I'm not sure how this affects Paul Levy's point, but I guess that I'll let Paul speak on that. -- Toby From rrosebru@mta.ca Mon Feb 27 19:30:38 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 19:30:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDrgf-0000FA-Pv for categories-list@mta.ca; Mon, 27 Feb 2006 19:21:53 -0400 Date: Mon, 27 Feb 2006 14:09:44 +0000 (GMT) From: Paul B Levy To: categories@mta.ca Subject: categories: Re: intuitionism and disjunction In-Reply-To: <200602271326.k1RDQb3K008051@saul.cis.upenn.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: 32 I agree that intuitionistic logic satisfies the disjunction property. But I don't see why this should make disjunction a more peripheral part of intuitionistic logic than implication. Paul > Paul Levy asks how the original intuitionists viewed disjunction. I > don't know how to say it better than this paragraph from Wikipedia > (anyone know who wrote it?). > > The disjunction and existence properties are validated by > intuitionistic logic and invalid for classical logic; they are key > criteria used in assessing whether a logic is constructive.... The > disjunction property is a finitary analogue, in an evident sense. > Namely given two or finitely many propositions P_i, whose > disjunction is true, we want to have an explicit value of the index > i such that we have a proof of that particular P_i. There are quite > concrete examples in number theory where this has a major effect. > > It is a (meta)theorem that in free Heyting algebras and free topoi > (and all sorts of variations thereon) that the disjunction property > holds. In the free topos that translates to the statement that the > terminator, 1, is not the join of two proper subobjects. Together with > the existence property it translates to the assertion that 1 is an > indecomposable projective object -- the functor it represents (i.e. > the global-section functor) preserves epis and coproducts. (And with > a little more work one can show it also preserves co-equalizers.) > > > -- Paul Blain Levy email: pbl@cs.bham.ac.uk School of Computer Science, University of Birmingham Birmingham B15 2TT, U.K. tel: +44 121-414-4792 http://www.cs.bham.ac.uk/~pbl From rrosebru@mta.ca Mon Feb 27 19:30:38 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 19:30:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDrhu-0000KE-3z for categories-list@mta.ca; Mon, 27 Feb 2006 19:23:10 -0400 Message-ID: <44030AFB.3060709@inf.ed.ac.uk> Date: Mon, 27 Feb 2006 15:21:47 +0100 From: Alberto Momigliano User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc4 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CFP: LFMTP 2006 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 33 ----------------------------------------------------------------------- International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP'06) http://www.cs.mcgill.ca/~bpientka/lfmtp06/index.html Affiliated with LICS and IJCAR at FLOC'06 Seattle, Washington, 16 August, 2006. CALL FOR PAPERS Important Dates: Submission deadline: 15 May 2006 Author Notification: 15 June 2006 Final Version: 15 July 2006 ----------------------------------------------------------------------- LFMTP'06 merges the International workshop on Logical Frameworks and Meta-languages (LFM) and the MERLIN workshop on MEchanized Reasoning about Languages with variable BIndingIN). Logical frameworks and meta-languages form a common substrate for representing, implementing, and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design and implementation on one hand and their applications, for example, to proof-carrying code have been the focus of considerable research over the last two decades. This workshop will bring together designers, implementors, and practitioners to discuss all aspects of logical frameworks. The broad subject areas of LFMTP'06 are: * The automation and implementation of the meta-theory of programming languages and related calculi, particularly work which involves variable binding and fresh name generation. * The theoretical and practical issues concerning the encoding of variable binding and fresh name generation, especially the representation of, and reasoning about, datatypes defined from binding signatures. * Case studies of meta-programming, and the mechanization of the (meta)theory of programming languages and calculi. Papers focusing on experiences with encoding programming languages theory and instances of proof-carrying code or proof-carrying authorization are particularly welcome. Topics include, but are not limited to: * logical framework design * meta-theoretic analysis * applications and comparative studies * implementation techniques * efficient proof representation and validation * proof-generating decision procedures and theorem provers * proof-carrying code * sub-structural frameworks * semantic foundations * methods for reasoning about logics * case studies. Invited Speaker: Gordon Plotkin (University of Edinburgh). Program Committee: Andrew Appel Princeton University Thierry Coquand Goteborg University Martin Hofmann LMU Munich Furio Honsell University of Udine Dale Miller Inria Futurs Brigitte Pientka McGill University Andrew Pitts Cambridge University Kevin Watkins Carnegie Mellon University Paper Submissions. Three categories of papers are solicited: * Category A: Detailed and technical accounts of new research: up to fifteen pages including bibliography. * Category B: Shorter accounts of work in progress and proposed further directions, including discussion papers: up to eight pages including bibliography. * Category C: System descriptions, presenting an implemented tool and its novel features: up to six pages. A demonstration is expected to accompany the presentation. Submission is electronic in postscript or PDF format. Submitted papers must conform to the ENTCS style, preferably using LaTeX2e. For further information and submission instructions, see the LFMTP web page: http://www.cs.mcgill.ca/~bpientka/lfmtp06/index.html Proceedings are to be published as a volume in the Electronic Notes in Theoretical Computer Science (ENTCS) series and will be available to participants at the workshop. Organizers: Brigitte Pientka Alberto Momigliano bpientka@cs.mcgill.ca amomigl1@inf.ed.ac.uk School of Computer Science LFCS, School of Informatics McGill University University of Edinburgh From rrosebru@mta.ca Mon Feb 27 19:30:38 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Feb 2006 19:30:38 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FDrjm-0000SG-T4 for categories-list@mta.ca; Mon, 27 Feb 2006 19:25:06 -0400 Date: Mon, 27 Feb 2006 14:10:52 -0600 (CST) From: Eugenia Cheng To: categories@mta.ca Subject: categories: Mac Lane Conference: third announcement Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 34 Dear All, This is the third announcement for the conference in memory of Saunders Mac Lane, at the University of Chicago, April 7 through April 11 2006. To register, please send an e-mail to Eugenia Cheng at the above address. ACCOMMODATION DEADLINE Please note the approaching deadline: special room rates at the Ramada are available until March 6. Note that cancellation incurs no fee provided you give at least 24 hours' notice. The phone number is +1-773-288-5800; apologies for the error in the previous announcement. For further information including updated travel information, current list of participants and previous announcements please see http://www.math.uchicago.edu/~eugenia/maclane We look forward to seeing you in April. With best regards, The organisers Peter May Eugenia Cheng From rrosebru@mta.ca Tue Feb 28 20:35:36 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Feb 2006 20:35:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FEFA9-0007i1-Kh for categories-list@mta.ca; Tue, 28 Feb 2006 20:25:53 -0400 Message-ID: <4403FFE2.7050302@inf.u-szeged.hu> Date: Tue, 28 Feb 2006 08:46:42 +0100 From: Computer Science Logic '06 Conference User-Agent: Mozilla Thunderbird 1.0 (Windows/20041206) MIME-Version: 1.0 To: categories@mta.ca Subject: categories: CSL'06 FINAL CALL FOR PAPERS Content-Type: text/plain; charset=ISO-8859-2; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 35 ********************************************************************** * CSL'06 * * Annual Conference of the European Association for * * Computer Science Logic * * September 25 -- 29, 2006, Szeged, Hungary * * http://www.inf.u-szeged.hu/~csl06/ * * CALL FOR PAPERS * ********************************************************************** Computer Science Logic (CSL) is the annual conference of the European Association for Computer Science Logic (EACSL). The conference is intended for computer scientists whose research activities involve logic, as well as for logicians working on issues significant for computer science. CSL'06, the 15th annual EACSL conference will be organized by the Institute of Informatics, University of Szeged. Suggested topics of interest include: automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and formal logics, modal and temporal logic, model checking, logical aspects of computational complexity, finite model theory, computational proof theory, logic programming and constraints, lambda calculus and combinatory logic, categorical logic and topological semantics, domain theory, database theory, specification, extraction and transformation of programs, logical foundations of programming paradigms, verification of security protocols, linear logic, higher-order logic, nonmonotonic reasoning, logics and type systems for biology. Programme Committee: Invited speakers: Krzysztof Apt(Amsterdam/Singapore) Martin Escardo (Birmingham) Matthias Baaz (Vienna) Paul-Andre Mellies (Paris) Michael Benedikt (Chicago) Luke Ong (Oxford) Pierre-Louis Curien (Paris) Luc Segoufin (Orsay) Rocco De Nicola (Florence) Miroslaw Truszczynski(Lexington,KY) Zoltan Esik (Szeged, chair) Dov Gabbay (London) Fabio Gadducci (Pisa) Organizing Committee: Neil Immerman (Amherst) Michael Kaminski (Haifa) Bakhadyr Khoussainov (Auckland) Zoltan Esik (Szeged, co-chair) Ulrich Kohlenbach (Darmstadt) Zsolt Gazdag (Szeged) Marius Minea (Timisoara) Eva Gombas (Szeged, co-chair) Damian Niwinski (Warsaw) Szabolcs Ivan (Szeged) R. Ramanujam (Chennai) Zsolt Kakuk (Szeged) Philip Scott (Ottawa) Zoltan L. Nemeth (Szeged) Philippe Schnoebelen (Cachan) Sandor Vagvolgyi Alex Simpson (Edinburgh) (Szeged, workshop-chair) Proceedings will be published in the LNCS series. Each paper accepted by the Programme Committee must be presented at the conference by one of the authors, and final copy prepared according to Springer's guidelines. Submitted papers must be in Springer's LNCS style and of no more than 15 pages, presenting work not previously published. They must not be submitted concurrently to another conference with refereed proceedings. The PC chair should be informed of closely related work submitted to a conference or journal by 1 April, 2006. Papers authored or coauthored by members of the Programme Committee are not allowed. Submitted papers must be in English and provide sufficient detail to allow the Programme Committee to assess the merits of the paper. Full proofs may appear in a technical appendix which will be read at the reviewer's discretion. The title page must contain: title and author(s), physical and e-mail addresses, identification of the corresponding author, an abstract of no more than 200 words, and a list of keywords. The submission deadline is in two stages. Titles and abstracts must be submitted by 24 April, 2006 and full papers by 1 May, 2006. Notifications of acceptance will be sent by 12 June, 2006, and final versions are due 3 July, 2006. A submission server will be available from 15 March, 2006. The Ackermann Award for 2006 will be presented to the recipients at CSL'06. Important Dates: Submission - title & abstract: 24 April, 2006 - full paper: 1 May, 2006 Notification: 12 June, 2006 Final papers: 3 July, 2006 Conference address: CSL'06 c/o Prof. Zoltan Esik Institute of Informatics, University of Szeged H-6701, Szeged, P.O.B. 652, Hungary web site: http://www.inf.u-szeged.hu/~csl06/ e-mail: csl06@inf.u-szeged.hu phone: +36-62-544-289 or +36-62-544-205 fax: +36-62-544-895 or +36-62-546-397 ********************************************************************** ********************************************************************** From rrosebru@mta.ca Tue Feb 28 20:35:36 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Feb 2006 20:35:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FEFBR-0007mr-IP for categories-list@mta.ca; Tue, 28 Feb 2006 20:27:13 -0400 From: "Ronald Brown" To: Subject: categories: Charles Ehresmann Date: Tue, 28 Feb 2006 10:35:45 -0000 MIME-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1";Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: RO X-Status: X-Keywords: X-UID: 36 This is to advertise my article: Three themes in the work of Charles Ehresmann: local-to-global; groupoids; higher dimensions. available on arXiv:math.DG/0602499 and to appear in the Proceedings of the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland) Banach Centre Publications. There is a discussion on http://www.math.columbia.edu/~woit/wordpress/?p=352 Ronnie Brown www.bangor.ac.uk/r.brown From rrosebru@mta.ca Tue Feb 28 20:35:36 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Feb 2006 20:35:36 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FEFE6-0000CV-C9 for categories-list@mta.ca; Tue, 28 Feb 2006 20:29:58 -0400 To: categories list Subject: categories: Re: Undirected graphs citation Date: Tue, 28 Feb 2006 18:01:56 -0500 From: wlawvere@buffalo.edu Message-ID: <1141167716.4404d6642a4f8@mail2.buffalo.edu> References: <440335A6.3050806@cs.stanford.edu> In-Reply-To: <440335A6.3050806@cs.stanford.edu> X-Mailer: University at Buffalo WebMail Cyrusoft SilkyMail v1.1.11 MIME-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 8bit Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 37 Bob Rosebrugh and I use that point of view explicitly in our book Set for Mathematics, but it is also in my paper "Qualitative distinctions..."graphs". Many of the more precise papers on combinatorics carefully describe each piece of the graph structure without noting that this amounts to a presentation of the monoid of endomaps of the 2 element set (which of course suffices). A similar lacuna of explicitness occurs in many papers on Galois theory where pregroupoids are an intermediate step ; the description of the pregroupoid concept is really just a presentation of the monoid of endomaps of the 4-element set. (A right action of that monoid is a groupoid if it satisfies the evident pullback condition on the action of the idempotents, the associative law being a case of the well-definedness of higher composition.) Quoting Vaughan Pratt : > What would be an early reference for the representation of > undirected > graphs (of the set-enriched rather than {0,1}-enriched kind) as > presheaves on the full subcategory 1 and 2 of Set? > > Vaughan Pratt > > > >