*mbx* 3bb593ef0000002b 1-Sep-2001 13:32:37 -0300,3032;000000000000-00000001 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f81G7ZV07477 for categories-list; Sat, 1 Sep 2001 13:07:35 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: "Sober Spaces and Continuations" (draft paper) Message-Id: From: Paul Taylor Date: Sat, 01 Sep 2001 16:21:14 +0100 X-Ident: pt Sender: cat-dist@mta.ca Precedence: bulk This is to invite your comments on Sober Spaces and Continuations Paul Taylor http://www.dcs.qmul.ac.uk/~pt/ASD/ (Please note that a lot of work has been done on this since the version that was put on the web without advertisement on 16 August.) A topological space is sober if it has exactly the points that are dictated by its open sets. We explain the analogy with the way in which computational values are determined by the observations that can be made of them. We propose a new definition of sobriety formulated in terms of lambda calculus and elementary category theory, with no reference to lattice structure, but show that, for topological spaces, this coincides with the standard lattice-theoretic definition. We show how to extend the primitive symbolic or categorical structure to make its types sober. For the natural numbers, the additional structure provides definition by description and general recursion. This is NOT ``denotational semantics of continuations using sober spaces'', though that could easily be derived. On the contrary, this paper provides the underlying lambda-calculus on the basis of which abstract Stone duality will re-axiomatise general topology. I would like to hear your comments on any of the following points: * intuitions about what it means to determine a computational value by making observations of it; * the categorical construction that is in Hayo Thielecke's thesis; * the "sober lambda calculus" that I derive from it; * re-axiomatisation of general topology using this, and in particular my notions of "prime" and "sober" expressed in the lambda calculus; * Russell's theory of descriptions, and general recursion; * computational effects that arise from Thielecke's "force". This paper serves as an introduction to my "Abstract Stone Duality" programme. However, it does NOT do the monadic construction either categorically or in terms of the "axiom of comprehension" that I presented at the APPSEM meeting in Darmstadt in March. I am currently writing these up in another paper, provisionally called "Comprehension in ASD". (I started to "get the upper hand" with the details of the proofs of the normalisation theorem about two weeks ago, and hope to be able to release a version containing all the maths, but not the narrative, before the teaching year starts again. Paul 1-Sep-2001 16:54:54 -0300,1454;000000000001-00000002 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f81JXLi10256 for categories-list; Sat, 1 Sep 2001 16:33:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 30 Aug 2001 18:19:11 +0100 (BST) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: Re: the alpha of Omega In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *15cVT0-0007ae-00*SozQcS5NZmU* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk On Mon, 27 Aug 2001, Keith Harbaugh wrote: > While the topic of topos subobject classifier is current, > how far back can the historical and conceptual origins > of the use of "$\Omega$" as the symbol denoting such be traced? > > Regards, > Keith Harbaugh > I seem to recall being told that it occurs somewhere in the original (mimeographed) version of SGA4 (as an interesting example of a sheaf on a site), and that Lawvere and Tierney borrowed the notation that Grothendieck et al. had used for it. However, I've never been able to find it there myself; I'm pretty sure it's not in the revised version published in Springer Lecture Notes. Peter Johnstone 5-Sep-2001 10:00:26 -0300,3702;000000000000-00000003 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f85CTJU26348 for categories-list; Wed, 5 Sep 2001 09:29:19 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: Uffe Henrik Engberg MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Message-ID: <15254.3284.450613.918032@harald.daimi.au.dk> Date: Wed, 5 Sep 2001 13:30:28 +0200 To: categories@mta.ca Subject: categories: CFP: FOSSACS'2002 X-Mailer: VM 6.90 under Emacs 20.7.1 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f85BUZb28179 Sender: cat-dist@mta.ca Precedence: bulk CALL FOR PAPERS Foundations of Software Science and Computation Structures (FOSSACS'2002) April 6 - 14, 2002 Grenoble, France URL: http://www.brics.dk/fossacs02 A member conference of the European Joint Conferences on Theory and Practice of Software (ETAPS'2002) URL: http://www-etaps.imag.fr/ CONFERENCE DESCRIPTION FOSSACS seeks papers which offer progress in foundational research with a clear significance to Software Sciences. Central objects of interest are the algebraic, categorical, logical, and geometric theories, models, and methods which support the specification, synthesis, verification, analysis, and transformation of sequential, concurrent, distributed, and mobile programs and software systems. Topics covered are semantic and syntactic foundations of Computation and Software Sciences, for instance: Computation processes over discrete and continuous data, methods and techniques for their manipulation, and analysis of their algorithmic properties. Type theory, domain theory, category theory. Models of concurrency, and corresponding calculi, algebras, and logics. Techniques for proving properties of protocols. Formal descriptions of general frames for the integration of specification techniques. SUBMISSION See http://www.brics.dk/fossacs02 for further details. In brief, papers must - be in English - present original research which is unpublished and not submitted elsewhere - be no more than 15 pages long in Springer-Verlag format - be submitted electronically in Postscript/PDF form (contact the chair if this is impossible) IMPORTANT DATES October 19, 2001 Submission deadline December 14, 2001 Notification of acceptance/rejection January 18, 2002 Camera-ready version due April 6 - 14, 2002 Conference dates INVITED SPEAKER The invited speaker at FOSSACS'2002 will be prof. Bruno Courcelle, LaBRI, Université Bordeaux. PROGRAM COMMITTEE David Basin (Freiburg, Germany) Julian Bradfield (Edinburgh, UK) Thomas Erhard (Marseille, France) Marcelo Fiore (Cambridge, UK) Carl Gunter (Upenn, USA) Furio Honsell (Udine, Italy) Mogens Nielsen, chair (Aarhus, Denmark) Fernando Orejas (Barcelona, Spain) Antoine Petit (Cachan, France) Frank Pfenning (CMU, USA) Sanjiva Prasad (IIT Delhi, India) Vladimiro Sassone (Sussex, UK) Andrzej Tarlecki (Warsaw, Poland) Frits Vaandrager (Nijmegen, Holland) Martin Wirsing (München, Germany) CONTACT Mogens Nielsen BRICS, Department of Computer Science University of Aarhus Ny Munkegade Bldg 540 8000 Aarhus Denmark email: fossacs02@brics.dk Tel/Fax: +45 8942 3260/3255 5-Sep-2001 10:00:34 -0300,2016;000000000000-00000004 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f85COeI32014 for categories-list; Wed, 5 Sep 2001 09:24:40 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: selinger@Theory.Stanford.EDU (Peter Selinger) Message-Id: <200109022156.OAA24811@theory-lab1.Stanford.EDU.theory> Subject: categories: Re: "Sober Spaces and Continuations" (draft paper) To: categories@mta.ca Date: Sun, 2 Sep 2001 14:56:55 -0700 (PDT) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Paul Taylor wrote: > This is to invite your comments on > > Sober Spaces and Continuations > > Paul Taylor > > http://www.dcs.qmul.ac.uk/~pt/ASD/ Dear Paul, thanks for your interesting article. I would like to point out that three relevant papers are missing from the references: [1] Fuehrmann, C. Direct-style and comtinuation-passing style models of control. See http://www.cs.bham.ac.uk/~cxf/research.htm. (1999). [2] Fuehrmann, C. Direct models of the computational lambda-calculus. In Proceedings of MFPS 15, ENTCS 20 (1999). [3] Selinger, P. Control categories and duality. MSCS 11:207-260 (2001). Many or all of your general categorical results (sections 3-4 and 6-7) appear in these papers. For instance, your notion of an object being "sober" (Def. 4.6) coincides with what Fuehrmann calls "satisfying Moggi's equalizing requirement", with associated theorems. I like the word "sober", because it is elegant and suggestive in this context, but Fuehrmann still deserves credit for the concept and the theorem. I liked the sections in which you apply these categorical methods to the category of locally compact topological spaces; it is interesting to see how the categorical concepts can be characterized in the concrete case. -- Peter 5-Sep-2001 10:01:28 -0300,831;000000000000-00000005 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f85CRFi29539 for categories-list; Wed, 5 Sep 2001 09:27:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <7AC902A40BEDD411A3A800D0B7847B660422AD49@sernt14.essex.ac.uk> From: "Wilkins, Elwood B" To: categories@mta.ca Subject: categories: Proof theoretic strength of topoi Date: Tue, 4 Sep 2001 15:49:50 +0100 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2653.19) Content-Type: text/plain; charset="iso-8859-1" Sender: cat-dist@mta.ca Precedence: bulk Hello, I'm looking for references on the proof-theoretic strength of the internal language of topoi. Can anyone help? Regards Elwood Wilkins 6-Sep-2001 15:47:50 -0300,2367;000000000001-00000006 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f86I45B11645 for categories-list; Thu, 6 Sep 2001 15:04:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 X-Sender: duskin@mail.buffnet.net Message-Id: In-Reply-To: References: Date: Sat, 1 Sep 2001 18:59:06 -0400 To: categories@mta.ca From: John Duskin Subject: categories: Re: the alpha of Omega Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk [note from moderator: apologies to Jack for the delayed posting...Bob] >On Mon, 27 Aug 2001, Keith Harbaugh wrote: > >> While the topic of topos subobject classifier is current, >> how far back can the historical and conceptual origins >> of the use of "$\Omega$" as the symbol denoting such be traced? >> >> Regards, >> Keith Harbaugh >> >I seem to recall being told that it occurs somewhere in the >original (mimeographed) version of SGA4 (as an interesting >example of a sheaf on a site), and that Lawvere and Tierney >borrowed the notation that Grothendieck et al. had used for it. >However, I've never been able to find it there myself; I'm >pretty sure it's not in the revised version published in >Springer Lecture Notes. > >Peter Johnstone -- I just got out my old original mimeographed copy of SGA 4 Fasicule 1 (by Verdier) and I'm afraid that I can't find it there either. Quite consistently, $\Omege$ is used there only to denote a generic topological space: " Soient $\Omega$ un espace topologique, $\Omega^{\tilde}$ le topos des faisceaux d'ensembles sur $\Omega$...." etc. Also I seem to recall hearing that when Grothendieck saw the Lawvere-Tierney subobject classifier $\Omega$ he was amazed that they could have missed the centrality of such a powerful notion in Topos Theory. He always subsequently referred to it technically as "the Lawvere element"! But to settle this, at least partly, why don't we just ask Bill or Myles to tell us where they got the $\Omega$ notation? Jack Duskin 6-Sep-2001 15:47:58 -0300,1981;000000000001-00000007 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f86I55T26706 for categories-list; Thu, 6 Sep 2001 15:05:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <3.0.6.16.20010831194057.43ffa43a@pop.cwru.edu> X-Sender: cxm7@pop.cwru.edu X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (16) Date: Fri, 31 Aug 2001 19:40:57 To: categories@mta.ca From: Colin McLarty Subject: categories: Re: the alpha of Omega Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk [note from moderator: apologies to Colin for delayed posting...Bob] "Dr. P.T. Johnstone" wrote of $\Omega$ as subobject classifier: >I seem to recall being told that it occurs somewhere in the >original (mimeographed) version of SGA4 (as an interesting >example of a sheaf on a site), and that Lawvere and Tierney >borrowed the notation that Grothendieck et al. had used for it. >However, I've never been able to find it there myself; I'm >pretty sure it's not in the revised version published in >Springer Lecture Notes. I have heard that too. And I am sure it is not in the published SGA4. I have one mimeographed version in my office. Omega does not occur there the sections on topologies, but next week I will look to see if it occurs as an example of a sheaf--unless someone who knows writes in sooner. best, Colin _________________________________________ Dialectic, the purest part of philosophy, hovers attentively over mathematics, encompasses its whole development, and of itself contributes to the special sciences their various perfecting, critical, and intellective powers--the powers, I mean, of analysis, division, definition, and demonstration. --Proclus, ca. 460 AD, A COMMENTARY ON THE FIRST BOOK OF EUCLID'S ELEMENTS 7-Sep-2001 11:25:48 -0300,4589;000000000000-00000008 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f87DtSk10500 for categories-list; Fri, 7 Sep 2001 10:55:28 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 6 Sep 2001 10:54:04 -0500 (EST) From: larry moss To: Subject: categories: CFP: Coalgebraic Methods in CS Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk [Apologies for multiple copies] CALL FOR PAPERS CMCS2002 5th International Workshop on Coalgebraic Methods in Computer Science Grenoble, France 6-7 April 2002 A satellite workshop of ETAPS 2002 Aims and Scope -------------- During the last few years, it is becoming increasingly clear that a great variety of state-based dynamical systems, like transition systems, automata, process calculi and class-based systems can be captured uniformly as coalgebras. Coalgebra is developing into a field of its own interest presenting a deep mathematical foundation, a growing field of applications and interactions with various other fields such as reactive and interactive system theory, object oriented and concurrent programming, formal system specification, modal logic, dynamical systems, control systems, category theory, algebra, analysis, etc. The aim of the workshop is to bring together researchers with a common interest in the theory of coalgebras and its applications. The topics of the workshop include, but are not limited to: the theory of coalgebras (including set theoretic and categorical approaches); coalgebras as computational and semantical models (for programming languages, dynamical systems, etc.); coalgebras in (functional, object-oriented, concurrent) programming; coalgebras and data types; (coinductive) definition and proof principles for coalgebras (with bisimulations or invariants); coalgebras and algebras; coalgebraic specification and verification; coalgebras and (modal) logic; coalgebra and control theory (notably of discrete event and hybrid systems). The workshop will provide an opportunity to present recent and ongoing work, to meet colleagues, and to discuss new ideas and future trends. Previous workshops of the same series have been organized in Lisbon, Amsterdam, Berlin, and Genova. The proceedings appeared as Electronic Notes in Theoretical Computer Science (ENTCS) Volumes 11,19, 33, and 41. You can get an idea of the types of papers presented at the meeting by looking at the tables of contents of the ENTCS volumes from the meetings, available at the ENTCS page. For venue, registration and suggested accommodation see the ETAPS2002 web page, http://www-etaps.imag.fr/ Submissions ----------- Submissions will be evaluated by the Program Committee for inclusion in the proceedings, which will be published in the ENTCS series. Papers must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Papers (of at most 15 pages) should be submitted electronically as uuencoded PostScript files at the address cmcs@cs.indiana.edu. A separate message should also be sent, with a text-only one-page abstract and with mailing addresses (both postal and electronic), telephone number and fax number of the corresponding author. Important Dates ---------------- Deadline for submission: 8 Janary 2002. Notification of acceptance: 20 February 2002. Final version due: 10 March 2002. Workshop dates: 6-7 April 2002. Program Committee ------------------- J. Adamek (Braunschweig) Alexandru Baltag (Amsterdam) Jesse Hughes (Nijmegen) H. Peter Gumm (Marburg) Alexander Kurz (Amsterdam) Bart Jacobs (Nijmegen) Marina Lenisa (Udine) Ugo Montanari (Pisa) Larry Moss (chair, Bloomington, IN) Ataru T. Nakagawa (Tokyo) John Power (Edinburgh) Horst Reichel (Dresden) Jan Rutten (Amsterdam) For more information --------------------- http://www.cs.indiana.edu/cmcs/ cmcs@cs.indiana.edu 7-Sep-2001 11:26:23 -0300,1416;000000000000-00000009 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f87DvnL07085 for categories-list; Fri, 7 Sep 2001 10:57:49 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Originating-IP: [128.205.248.226] From: "F. William Lawvere" To: categories@mta.ca Subject: categories: Re: the alpha of Omega Date: Fri, 07 Sep 2001 13:16:50 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 07 Sep 2001 13:16:51.0078 (UTC) FILETIME=[5B190A60:01C1379F] Sender: cat-dist@mta.ca Precedence: bulk Sorry I didn't reply sooner to this; I was enroute from Perugia to Buffalo. As I recall, the original omega was the sheaf of CLOSED sets on a topological space, in a paragraph devoted to applications to notions like sections with supports. Having recognized the importance of the subobject classifier, making the observation that isomorphic things probably would not remain notationally distinct forever, and especialy wanting not to change an "established"(!) symbol, we replaced the T (for truth) (which was used in my IAM 69 talk and ICM 70 paper). Thus the mega oh is a coincidence. Unfortunately I do not recall in which part of the prepublished SGA4 that paragraph occurs . 7-Sep-2001 11:27:39 -0300,1467;000000000000-0000000a Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f87Dug701801 for categories-list; Fri, 7 Sep 2001 10:56:42 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs Date: Fri, 7 Sep 2001 05:56:20 -0400 (EDT) From: Michael Barr X-Sender: barr@triples.math.mcgill.ca To: Categories list Subject: categories: injective modules in a topos Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk A week or so ago, I asked the question about injectives in a category of modules in over a ring object in a Grothendieck topos. I asked whether if I is an injective module and E is an object of the topos, I^E is injective. I got no useful answers. Here is a related question. Does anyone know if an injective is interally injective? That is, if A and B are modules, then there is an object of the topos A -o B that is the subobject of B^A consisting of the additive morphisms. So what I am asking is whether for an injective I, the induced B -o I --> A -o I is epic. Or rather, can every module be embedded into an internal injective? Is there an internally injective cogenerator? Michael 7-Sep-2001 11:29:01 -0300,6281;000000000001-0000000b Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f87DuLi28806 for categories-list; Fri, 7 Sep 2001 10:56:21 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: lhe@127.0.0.1 Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Date: Thu, 6 Sep 2001 22:18:39 +0200 To: Recipient List Suppressed:; From: Lars-Henrik Eriksson Subject: categories: CFP: FME'2002 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f86M4Bb10437 Sender: cat-dist@mta.ca Precedence: bulk apologies if you receive multiple copies... Please forward to interested collegues. FORMAL METHODS EUROPE FME 2002 "Formal Methods: Getting IT Right" International Symposium and Tutorials http://floc02.diku.dk/FME/ 20-24 July 2002 Call for Papers *************** FME 2002 is the eleventh in a series of symposia organised by Formal Methods Europe, an independent association whose aim is to stimulate the use of, and research on, formal methods for software development. These symposia have been notably successful in bringing together a community of users, researchers, and developers of precise mathematical methods for software development. In 2002 the symposium will be held in conjunction with the third Federated Logic Conference (FLoC'02) in Copenhagen, Denmark. The theme of FME 2002 is Formal Methods: Getting IT Right. The double meaning is intentional. On the one hand, the theme acknowledges the significant contribution formal methods can make to Information Technology, by enabling computer systems to be described precisely and reasoned about with rigour. On the other hand, it recognises that current formal methods are not perfect, and further research and practice are required to improve their foundations, applicability and effectiveness. FME seeks papers in all aspects of formal methods for computer systems, including the following: * theoretical foundations * practical use and case studies * specification and modelling techniques * software development and refinement * tool support and software engineering environments for formal methods * verification and validation * hidden formal methods, and making benefits available to non-experts * reusable domain theories * method integration * hardware verification In addition to presentations of submitted papers, the symposium will offer tutorials, workshops, invited speakers, and tool demonstrations. PAPERS Full papers should be submitted in Postscript or PDF format by e-mail to reach the Program Co-chairs by 15 January 2002. Papers will be refereed by the Program Committee and must be original research papers that have not been submitted elsewhere for publication. Accepted papers will be published in the symposium proceedings. Papers should not exceed twenty pages, although longer papers will be considered if their content justifies it. LNCS format should be used: see http://www.springer.de/comp/lncs/authors.html for details. Please include a short list of keywords on a separate line at the end of the abstract, beginning with the word "Keyword:" in boldface. OTHER SYMPOSIUM ACTIVITIES Tutorials and workshops will be held on 20-21 July 2002. Each tutorial will last one-half or one day. Proposals are welcome, and should be directed to the Program Co-chairs by 15 January 2002; more details will appear on the web-site above. Tool demonstrations will also take place during the symposium, with the opportunity for presentations to be made about each tool. Proposals for tool demonstrations should be made to the Tool Demonstration Coordinator, with whom provison of necessary computing facilities should be discussed. PEOPLE Organising Chair Dines Bjřrner Informatics and Mathematical Modelling Building 322, Richard Petersens Plads Technical University of Denmark DK-2800 Lyngby, Denmark Tel: +45 4525 3720 Email: db@imm.dtu.dk Programme Co-chairs Lars-Henrik Eriksson, Industrilogik L4i AB Box 21024, SE-100 31 Stockholm, Sweden Tel: +46 1859 1690 Fax: +46 1847 17058 Email: lhe@L4i.se Peter Lindsay, Software Verification Research Centre The University of Queensland, Queensland 4072, Australia Tel: +61 7 3365 2005 Fax: +61 7 3365 1533 Email: Peter.Lindsay@svrc.uq.edu.au Programme Committee Bernhard Aichernig Graz University of Technology, Austria Juan Bicarregui SERC Rutherford Labs, UK Ernie Cohen Telcordia Technologies, USA Ben Di Vito NASA Langley Research Center, USA Cindy Eisner IBM Haifa Research Laboratory, Israel Lars-Henrik Eriksson (co-chair) Industrilogik, Sweden John Fitzgerald Transitive Technologies Ltd, UK Jim Grundy Intel Corporation, USA Yves Ledru LSR/IMAG, Domaine Universitaire, France Peter Lindsay (co-chair) University of Queensland, Australia Markus Montigel University of New Orleans, USA Richard Moore IFAD, Denmark Tobias Nipkow Technische Universität München, Germany Colin O'Halloran Qinetiq (ex-DERA), UK Jose Oliveira Universidade do Minho, Portugal Nico Plat West Consulting, The Netherlands Jeannette Wing Carnegie Mellon University, USA Jim Woodcock Oxford University, UK Joakim von Wright Ĺbo Akademi University, Finland Pamela Zave AT&T Laboratories, USA Tool Demonstration Coordinator Paul Mukherjee The Institute of Applied Computer Sciense (IFAD) Forskerparken 10, DK-5230 Odense M, Denmark Tel: +45 6315 7131 Fax: +45 6593 2999 Email: paul.mukherjee@ifad.dk IMPORTANT DATES Submission of papers, tutorial proposals and workshop proposals: 15 January 2002 Notification of acceptance/rejection: 27 March 2002 Camera ready final version of papers due: 10 May 2002 7-Sep-2001 13:09:25 -0300,2260;000000000000-0000000c Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f87Fdgj14782 for categories-list; Fri, 7 Sep 2001 12:39:42 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: Re: injective modules in a topos Message-Id: From: Paul Taylor Date: Fri, 07 Sep 2001 15:47:01 +0100 X-Ident: pt Sender: cat-dist@mta.ca Precedence: bulk Mike Barr asks > Does anyone know if an injective is internally injective? I cannot contribute anything to the question about rings and modules, but I have recently had to think about this problem in the context of (my re-axiomatisation of) topological spaces. We want any subspace to have the "subspace topology". This is the same as saying that the Sierpinski space is injective with respect to subspace inclusions (regular monos, if you please). In my setting I think of the topology (the lattice of open sets) not as a lattice over the category of sets, but as a space with the Scott topology. The "internal injectivity" property in this situation is therefore that we have a retraction i U >-----------> X I U >--------> X Sigma Sigma <<-------- i Sigma but if the map I is "internal" then this is a Scott-continuous map, and we only have certain kinds of subspaces. Particularly annoyingly, we cannot form the intersection of two such subspaces. This is what I am currently writing up, as the successor to the paper "Sober Spaces and Continuations" that I advertised on Saturday. Now, if you interpret all of this in the traditional axiomatisation of topology or locale theory, all of this only makes sense for locally compact spaces anyway. My "monadic" axiomatisation does this more abstractly, but with locally compact spaces as the motivating model. The intersection problem is clearly an undesirable feature of this theory, and I believe that the "internal" injectivity is the flaw. Paul http://www.dcs.qmul.ac.uk/~pt/ASD 7-Sep-2001 13:21:00 -0300,1392;000000000001-0000000d Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f87FcMu20202 for categories-list; Fri, 7 Sep 2001 12:38:22 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 7 Sep 2001 16:42:48 +0200 (DFT) From: Jean-Pierre Cotton To: categories@mta.ca Subject: categories: Vector lattices Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Dear categorists I am interested in applications of category theory to probability , fuzzy sets and statistical theory. A useful concept is that of "probability hilbert spaces" (see the book "Hilbert space methods in probability and statistical inference" by small and Mc Leish, Ed Wiley), that is Hilbert space with additional lattice structure and some compatibility betwen the two structures. This can be seen as a category, the morphisms are maps preserving both structures. This is also a particular case of more general structures , those of Banach lattices and Riesz spaces , which are vector spaces with lattice structure. Does anyone know if those kinds of structures have been studied from a categorical point of view? Regards. J. P. Cotton. 10-Sep-2001 15:22:11 -0300,4690;000000000000-0000000e Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8AHR1021891 for categories-list; Mon, 10 Sep 2001 14:27:01 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3B9C9B39.4ED68A64@lcc.uma.es> Date: Mon, 10 Sep 2001 12:51:37 +0200 From: =?iso-8859-1?Q?Jos=E9?= Luis =?iso-8859-1?Q?Trivi=F1o?= X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.2.17 i686) X-Accept-Language: en MIME-Version: 1.0 To: categories Subject: categories: CFP: ICALP 2002 Content-Type: text/plain; charset=iso-8859-1 X-MIME-Autoconverted: from 8bit to quoted-printable by cartero.sci.uma.es id f8AB4IH15787 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f8AB5ub08108 Sender: cat-dist@mta.ca Precedence: bulk We apologize for possible multiple postings. In http://www.lcc.uma.es/icalp2002/c4p-sep01.pdf you can find a pdf version of this call for paper. +++++++++++++++++++++++++++++++++++++ Call for Papers ICALP 2002 29th International Colloquium on Automata, Languages and Programming July 8-13, 2002, Málaga, Spain Camera Ready: April 16, 2002 The 29th annual meeting of the European Association of Theoretical Computer Science will be held in Málaga, Spain, July 8-13, 2002 (at the E.T.S. Ingeniería Informática). As with the Journal Theoretical Computer Science (TCS), the scientific program of the Colloquium will be split into two parts: Track A of the meeting will correspond to Algorithms, Automata, Complexity and Games, while Track B to Logic, Semantics and Theory of Programming. SUBMISIONS: Authors are invited to submit extended abstract of their papers, presenting original contributions to the theory of computer science. Detailed instructions for paper submissions will be found on the conference webpage (http://www.lcc.uma.es/icalp2002) and in future calls for papers. Submissions should consist of: a cover page, with the author's full name, address, fax number, e-mail address, a 100-word abstract, keywords and to which track (A or B) the paper is being submitted and an extended abstract describing original research. At least one author of an accepted paper should be available to present it at the conference. Simultaneous submission to other conferences with published proceedings is not allowed. Further information (dates and instructions for submissions, workshops, registration, location and travel) will be provided in future announcements. ORGANIZING COMMITEE: Buenaventura Clares (University of Granada), Ricardo Conejo (University of Málaga), Inmaculada Fortes (University of Málaga), Llanos Mora (University of Málaga), Rafael Morales (co-Chair, University of Málaga), Marlon Nuńez (University of Málaga), José Luis Pérez de la Cruz (University of Málaga), Gonzalo Ramos (University of Málaga), Francisco Triguero (co-Chair, University of Málaga), José Luis Trivińo (University of Málaga). IMPORTANT DATES: Workshops proposal: November 8, 2001 Submissions: January 14, 2002 Notification: March 20, 2002 CONFERENCE CO-CHAIRS Prof. Francisco Triguero Prof. Rafael Morales Universidad de Málaga E.T.S. Ingeniería Informática Dept. Lenguajes y Ciencias de la Computación Bulevar Louis Pasteur, 35 29071 - Málaga (SPAIN) e-mail: icalp2002@informatica.uma.es PROGRAM COMMITEE Track A Ricardo Baeza-Yates (U. Chile) Volker Diekert (U. Stuttgart) Paolo Ferragina (U. Pisa) Catherine Greenhill (U. Melbourne) Torben Hagerup (U. Frankfurt) Johan Hĺstad (KTH, Stockholm) Gabriel Istrate (Los Alamos) Claire Kenyon (U. Paris XI) Der-Tsai Lee (Acad. Sinica, Taipei) Heikki Mannila (Nokia, Helsinki) Elvira Mayordomo (U. Zaragoza) Helmut Prodinger (U. Witwatersrand, South Africa) Jan van Leeuwen(U. Utrecht) Paul Vitányi (CWI, Amsterdam) Peter Widmayer (ETH Zürich) (Chair) Gerhard Woeginger (T.U. Graz) Christos Zaroliagis (U. Patras) Track B Martín Abadi (U. California, Santa Cruz) Roberto Amadio (U. Provence) Gilles Barthe (INRIA-SophiaAntipolis) Manfred Droste (University of Technology Dresden) Cédric Fournet (Microsoft Cambridge) Matthew Hennessy (U. Sussex) (Chair) Furio Honsell (U. Udine) Peter O'Hearn (Queen Mary & W. C. London) Fernando Orejas (U.P.Catalunya) Ernesto Pimentel (U. Málaga) David Sands (Chalmers University of Technology and Göteborg University) Dave Schmidt (U. Kansas) Gheorghe Stefanescu (U. Bucharest) Vasco Vasconcelos (U. Lisbon) Thomas Wilke (U. Kiel) 10-Sep-2001 15:31:10 -0300,3005;000000000000-0000000f Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8AHRRm12312 for categories-list; Mon, 10 Sep 2001 14:27:27 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: Ph.D.: ``Operational congruences for reactive systems'' From: James Leifer Date: Mon, 10 Sep 2001 14:16:14 +0200 Message-Id: <20010910121614.57EF64008@brouilly.inria.fr> Sender: cat-dist@mta.ca Precedence: bulk I'm pleased to announce that the following Ph.D. dissertation is now being distributed as a technical report and is available for download. -James Leifer INRIA Rocquencourt ================================================================= Author: James J. Leifer Title: ``Operational congruences for reactive systems'' Distribution: Ph.D. Dissertation and Technical Report 521, Computer Laboratory, University of Cambridge Supervisor: Robin Milner URL: http://pauillac.inria.fr/~leifer/ Abstract: The dynamics of process calculi, e.g. CCS, have often been defined using a labelled transition system (LTS). More recently it has become common when defining dynamics to use reaction rules ---i.e. unlabelled transition rules--- together with a structural congruence. This form, which I call a reactive system, is highly expressive but is limited in an important way: LTSs lead more naturally to operational equivalences and preorders. So one would like to derive from reaction rules a suitable LTS. This dissertation shows how to derive an LTS for a wide range of reactive systems. A label for an agent (process) a is defined to be any context F which intuitively is just large enough so that the agent Fa (``a in context F'') is able to perform a reaction. The key contribution of my work is the precise definition of ``just large enough'', in terms of the categorical notion of relative pushout (RPO), which ensures that several operational equivalences and preorders (strong bisimulation, weak bisimulation, the traces preorder, and the failurespreorder) are congruences when sufficient RPOs exist. I present a substantial example of a family of reactive systems based on closed, shallow action calculi (those with no free names and no nesting). I prove that sufficient RPOs exist for a category of such contexts. The proof is carried out indirectly in terms of a category of graphs and embeddings and gives precise (necessary and sufficient) conditions for the existence of RPOs. I conclude by arguing that these conditions are satisfied for a wide class of reaction rules. The thrust of this dissertation is, therefore, towards easing the burden of exploring new models of computation by providing a general method for achieving useful operational congruences. ================================================================= 10-Sep-2001 18:04:02 -0300,1686;000000000000-00000010 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8AJx0h27051 for categories-list; Mon, 10 Sep 2001 16:59:00 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <3.0.6.32.20010910141631.007e88a0@127.0.0.1> X-Sender: cxm7/pop.cwru.edu@127.0.0.1 X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (32) Date: Mon, 10 Sep 2001 14:16:31 -0400 To: categories@mta.ca From: Colin McLarty Subject: categories: Editions of SGA 4 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk I know of just two editions of SGA 4. Does anyone here know of others? There is the well known one by Springer, where SGA 4 gets three volumes. It came out after Lawvere and Tierney had axiomatized elementary toposes. Before that, there was an edition published by the IHES with no publication date titled: INSTITUT DES HAUTES ETUDES SCIENTIFIQUES SEMINAIRE DE GEOMETRIE ALGEBRIQUE 1963-64 COHOMOLOGIE ETALE DES SCHEMAS par Michael Artin et Alexander Grothendieck Fascicule 1 par Jean-Louis Verdier This volume consists of an "Avant-Propos" plus six exposes by Verdier: "Topologies et Faisceaux" I-IV, plus "Cohomologie etale des schemas" and "Etude des limites". The Avant-Propos describes the contents of later volumes, but I don't know if they ever appeared in this form. No doubt some notes circulated in some places even before that. Did anyone here see such notes? Does anyone here know of other editions of the whole? thanks, Colin 13-Sep-2001 17:57:05 -0300,6406;000000000000-00000012 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8DJQWg18285 for categories-list; Thu, 13 Sep 2001 16:26:32 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Wed, 12 Sep 2001 18:24:17 +0100 To: categories@mta.ca From: Giovanni Sambin Subject: categories: Second Workshop on Formal Topology, Venice, April 2002 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f8CGHkb07605 Sender: cat-dist@mta.ca Precedence: bulk SECOND WORKSHOP ON FORMAL TOPOLOGY Auditorium S. Margherita, Campo S. Margherita Venice, April 4-6, 2002 organised by: the EC Types Working Group Dipartimento di Matematica Pura e Applicata, Universita' di Padova Dipartimento di Informatica, Universita' Ca' Foscari, Venezia This workshop is about a specific approach to formal, or pointfree, topology, which stresses its constructive features. Its historical roots include Brouwer's conception of the continuum, which was expressed in terms of choice sequences. The later analysis and elimination of choice sequences led to connections with locale theory and inductive definitions, as in Martin-Loef's Notes on constructive mathematics. So it aims at a theory of formal spaces, in some way similar to the present impredicative theory of locales, but expressed in a predicative constructive framework such as constructive type theory (Martin-Loef) or constructive set theory (Aczel). As time passed, the landscape of formal topology has become wider, and its distinctive predicative foundation has given rise to some unexpected mathematical developments (even the right approach to the notion of a `closed set' needs a conceptually new approach, where `closed' is not the complement of `open'). Nowadays it includes a variety of themes and novelties, which are of interest in: - computer science, because of the methods of definition by induction and recently also by co-induction, the techniques for the extraction of constructive information from a priori non effective arguments and connections with domain theory, implementation problems, etc.; - logic and foundations, because of the interaction between the foundations of mathematics and the actual development of mathematics, methods from proof theory in the practice of mathematics, sheaf models, the logical nature of topological definitions, etc.; - mathematics itself, because of the process of constructivization - which often is accompanied by a conceptual simplification - of classical results of topology and of mathematics in general and also the connections with category theory and locale theory, etc.. The first workshop of this series took place in Padova, October 1997. It was widely appreciated for its relaxed and constructive atmosphere, and for an open discussion on various approaches. Hopefully with a similar atmosphere, the aim of the second workshop will be to obtain an up-to-date picture of the foundational and technical issues concerning formal topology, and to clarify the connections with related approaches. Invited speakers. The list of invited speakers at the moment includes Martin Escardo, Henri Lombardi, Peter Johnstone, Erik Palmgren, Mike Smyth, Steve Vickers. Tutorials. The workshop will be preceeded by one day, 3 April 2002, of tutorials to help those people who are interested but have little or even no knowledge of formal topology. At the moment, Peter Aczel and Giovanni Sambin have volunteered. Contributed papers. Those who wish to contribute with a half hour talk, should submit a summary of contents (from 1 to 10 pages) to Thierry Coquand, coquand@cs.chalmers.se by 28 February 2002. The program committe will notify acceptance by 15 March 2002. Proceedings. The proceedings will be published after the workshop, probably, a special issue of some good journal (hence with referees and open also to nonparticipants) Registration. Registration is free; the form below must be sent to Giovanni Curi, gcuri@math.unipd.it. A convenient accomodation in Venice can be provided only to those participants who register by 30 September 2001. For a low cost accomodation (possibily in a common room), contact Claudia Faggian claudia@math.unipd.it Grants. We also plan to offer a limited number of grants for students and young researchers covering accomodation and food. Please send a short CV and motivations for participation to Giovanni Sambin sambin@math.unipd.it Site. Venice needs no presentation. But note that the site of the workshop is out of the main tourist routes, and should allow for an appreciation of the popular and historical aspects of the city. We expect to find convenient accomodations nearby. Social Program. A trip will be organized for those who remain on Sunday 7 April 2002. An idea is to hire a boat and have lunch in an island of the lagoon. The full social program will be communicated later. Second announcment. The second announcement will contain information updates and the web address of a page dedicated to the workshop (with details on place, accomodation, tourist information, trip, etc.). The program committee Peter Aczel Thierry Coquand Per Martin-Loef (chair) Giovanni Sambin (local organization) Dieter Spreen dates: September 30, 2001 : early registration (with safe accomodation) February 28, 2002: deadline for the submission of papers March 15, 2002: program is decided April 3, 2002: tutorials April 4 - 6, 2002: workshop April 7: trip for those who wish to remain, probably on a privately hired boat Registration Form: Name and Family name: Institution: Address: E-mail address: Date of arrival: Date of departure: Kind of accomodation (if required): low cost (common room, around 8 beds, price around 15 euros) single room (Fondazione Levi or Palazzo Zenobio, price around 50 euros, maybe less) double-triple room (Fondazione Levi or Palazzo Zenobio, price around 35 euros) 14-Sep-2001 19:08:46 -0300,1222;000000000000-00000013 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8EJjmI15493 for categories-list; Fri, 14 Sep 2001 16:45:48 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3BA1EBFC.CB89D5A9@disi.unige.it> Date: Fri, 14 Sep 2001 13:37:32 +0200 From: rosolini@disi.unige.it X-Mailer: Mozilla 4.77 [en] (X11; U; Linux 2.4.3-12 i686) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: job: post-doc position at Genoa Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk The University of Genoa offers a one-year post-doc position to work on Realizability Semantics, with a main focus on the category-theoretic analysis of the models. Official information is available from http://www.unige.it/concorsi/assricerca/ or directly at http://www.disi.unige.it/person/RosoliniG/dr2063.rtf Please contact me if interested or just in need of a translation from Italian burocratese. G.Rosolini DISI, via Dodecaneso 35 16146 Genova, ITALY tel +39 010 3536630 rosolini@disi.unige.it 15-Sep-2001 11:21:57 -0300,2577;000000000001-00000014 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8FCkjS30791 for categories-list; Sat, 15 Sep 2001 09:46:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <00c301c13d5a$a2e1c2e0$060a000a@AVILCIUS> From: "Al Vilcius" To: Subject: categories: quantum cats Date: Fri, 14 Sep 2001 16:20:02 -0400 MIME-Version: 1.0 X-Priority: 3 Sender: cat-dist@mta.ca Precedence: bulk Can topos theory be used to enhance (rework?) our models of state space and its dynamics in quantum theory? There are two approaches I am aware of, specifically: 1) M. Adelman and J.V. Corbett. "A Sheaf Model for Intuitionistic Quantum Mechanics" Applied Categorical Structures. (1995)(3)(1) ref: ftp://ftp.mpce.mq.edu.au/pub/maths/murray and other related papers. 2) C.J. Isham and J.Butterfield, "Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity" ref: http://xxx.lanl.gov/abs/gr-qc/9910005 and related papers. Plus there is of course the fantastic n-category approach of John Baez http://www.math.ucr.edu/home/baez/ but I have no idea yet of how this relates to QM (any hints?). Has anyone done a comparison of these approaches ?, perhaps relating them to the idea of pasting together Boolean algebras in some "partial" structures, as outlined briefly in "Charting the labyrinth of quantum logics" by Hardegree / Frazer (1979). An intriguing picture (to me) that includes state space S is a ----> S -----> c where the (contravarient "over" S) left side represents actions, shapes (points), constructions and the (covarient "under" S) right side represents observations, destructions, attributes in an algebra/co-algebra framework. (there should also be an endo-arrow on S for dynamics, I guess, but I could not draw it here) Has anyone studied algebra/co-algebra models for QM? My interest is strictly personal (ie. I have no organized program) and actually arose from my attempts to understand what is being called quantum computing. I was compelled to dig deeper because I just cannot come to grips with "irreducible uncertainty", or more precisely: epistemological vs. ontological uncertainty (as differentiated by David Cohen '89), and why it is that we should model measurement using a (classical) continuum of real numbers (pointing to an SDG alternative perhaps). Your gentle guidance is appreciated. Al Vilcius 17-Sep-2001 10:16:26 -0300,2387;000000000001-00000015 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8HBFHV21024 for categories-list; Mon, 17 Sep 2001 08:15:17 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: baez@math.ucr.edu Message-Id: <200109152223.f8FMNfe26831@math-cl-n04.ucr.edu> Subject: categories: quantum cats To: categories@mta.ca (categories) Date: Sat, 15 Sep 2001 15:23:41 -0700 (PDT) X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Quantum cats? I assume we're not talking about Schrodinger's.... "Al Vilcius" writes: > Plus there is of course the fantastic n-category approach of John Baez > http://www.math.ucr.edu/home/baez/ > but I have no idea yet of how this relates to QM (any hints?). I got interested in n-categories precisely because I think they'll shed a lot of light on quantum gravity! Here are some papers where I try to explain why: Higher-dimensional algebra and topological quantum field theory, with James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105. (Not available electronically, since it contains lots of hand-drawn pictures.) Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189. Available as http://xxx.lanl.gov/abs/q-alg/9609018 Higher-dimensional algebra and Planck-scale physics, in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press, 2001. Available as http://xxx.lanl.gov/abs/gr-qc/9902017 >From finite sets to Feynman diagrams, with James Dolan, in Mathematics Unlimited - 2001 and Beyond, vol. 1, eds. Bj\"orn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-50. Available as http://arXiv.org/abs/math.QA/0004133 2-categories are also fundamental to my work on spin foam models of quantum gravity, but I have done my best to keep that fact secret, to avoid scaring the physicists: An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics, eds. Helmut Gausterer and Harald Grosse, Lecture Notes in Physics, Springer-Verlag, Berlin. Available as http://xxx.lanl.gov/abs/gr-qc/9905087 Best, John Baez 17-Sep-2001 15:59:36 -0300,7087;000000000001-00000016 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8HES5A02523 for categories-list; Mon, 17 Sep 2001 11:28:05 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Content-Type: text/plain; charset="iso-8859-1" From: Mark Minas Reply-To: Mark.Minas@informatik.uni-erlangen.de Organization: University of Erlangen, CS Dep. Subject: categories: CFP: Diagrams 2002 Date: Fri, 14 Sep 2001 14:26:07 +0200 X-Mailer: KMail [version 1.2] MIME-Version: 1.0 Message-Id: <01091414253303.24746@faui24l> Content-Transfer-Encoding: 8bit To: "Mark Minas" Sender: cat-dist@mta.ca Precedence: bulk Sorry if some of you receive multiple copies of this message. Mark Minas ------------------------------------------------------------------ Call for Papers Diagrams 2002 Second International Conference on Theory and Application of Diagrams Callaway Gardens & Resort, Georgia, USA, April 18-20, 2002 Conference information: http://kogs-www.informatik.uni-hamburg.de/~d2k2/ Location information: http://www.callawaygardens.com -------------------------------------------------------------------- "Diagrams" is an international and interdisciplinary conference series on the theory and application of diagrams in any scientific field of enquiry. From early human history, diagrams have been pervasive in human communication. The recent rise of multimedia technology that has turned advanced visual communication into an integral part of our everyday reality makes a better understanding of the role of diagrams and sketches in communication, cognition, creative thought, and problem-solving a necessity. These developments have triggered a new surge of interest in the study of diagrammatic notations, which is driven by several different scientific disciplines concerned with cognition, computation and communication. The study of diagrammatic communication as a whole must be pursued as an interdisciplinary endeavor. "Diagrams 2002" is the second event in this conference series, which was successfully launched in Edinburgh in September 2000. It attracts a large number of researchers from virtually all academic fields that are studying the nature of diagrammatic representations, their use in human communication, and cognitive or computational mechanisms for processing diagrams. By combining several earlier workshop and symposia series that were held in the US and Europe [Reasoning with Diagrammatic Representations (DR), US; Thinking with Diagrams (TWD), Europe; Theory of Visual Languages (TVL), Europe], "Diagrams" has emerged as a major international conference on this topic. It is the only conference that provides a united forum for all areas that are concerned with the study of diagrams: architecture, artificial intelligence, cartography, cognitive science, computer science, education, graphic design, history of science, human-computer interaction, linguistics, philosophical logic, and psychology, to name a few. Topics of interest include but are not limited to: * computational models of reasoning with and interpretation of diagrams * diagram understanding by humans or machines * diagram usage in scientific discovery * formalization of diagrammatic notations * history of diagrammatic languages and notations * interactive graphical communication * novel uses of diagrammatic notations * psychological issues pertaining to perception, comprehension, and production of diagrams * reasoning with diagrammatic representations * role of diagrams in applied areas such as visualization * spatial information and diagrams * usability issues concerning diagrams "Diagrams 2002" will consist of technical sessions with presentations of refereed papers, posters and tutorial sessions. The tutorials will provide introductions to diagram research in various disciplines in order to foster a lively interdisciplinary exchange. We invite submissions of tutorial proposals, full research papers and extended abstracts of posters. All submissions will be fully peer reviewed and accepted papers and posters will be published in the conference proceedings. Further information and submission details will be available from the conference web site: http://kogs-www.informatik.uni-hamburg.de/~d2k2/ Important Dates: ***************** Deadline for submission of abstracts: Friday November 2, 2001 Deadline for submission of full versions: Friday November 16, 2001 Notification of authors: Friday January 11, 2002 Camera ready copies due: Friday January 25, 2002 Deadline for early registration: Friday March 1, 2002 Conference dates: Thursday April 18 - Saturday April 20, 2002 General Chair: N. Hari Narayanan, Auburn University & Georgia Tech (USA) Program Chairs: Mary Hegarty, UC Santa Barbara (USA), Bernd Meyer, Monash University (Australia) Local Chair: Roland Hubscher, Auburn University (USA) Publicity Chair: Volker Haarslev, University of Hamburg (Germany) Program Committee: Michael Anderson, University of Hartford, USA Dave Barker-Plummer, Stanford University, USA Alan Blackwell, Cambridge University, UK Dorothea Blostein, Queen's University, Canada Paolo Bottoni, University of Rome, Italy Jo Calder, Edinburgh University, UK B. Chandrasekaran Ohio State University, USA Peter Cheng, University of Nottingham, UK Richard Cox, Sussex University, UK Max J. Egenhofer, University of Maine, USA Norman Foo, University of Sydney, Australia Ken Forbus, Northwestern University, USA George Furnas, University of Michigan, USA Meredith Gattis, University of Sheffield, UK Helen Gigley Office of Naval Research, USA Mark Gross, University of Washington, USA Corin Gurr, Edinburgh University, UK Volker Haarslev, University of Hamburg, Germany Patrick Healey, University of London, UK Mary Hegarty, University of California, USA John Howse, University of Brighton, UK Roland Hubscher, Auburn University, USA Maria Kozhevnikov, Rutgers University, USA Zenon Kulpa, Institute of Fundamental Technological Research, Poland Stefano Levialdi, University of Rome, Italy Robert Lindsay, University of Michigan, USA Ric Lowe, Curtin University, Australia Bernd Meyer, Monash University, Australia Richard Mayer, University of California, USA Mark Minas, University of Erlangen, Germany Hari Narayanan, Auburn University & Georgia Tech, USA Kim Marriott, Monash University, Australia Nancy Nersessian, Georgia Tech, USA Daniel Schwartz, Stanford University, USA Priti Shah, University of Michigan, USA Atsushi Shimojima, Japan Advanced Institute of Science and Technology, Japan Sun-Joo Shin, University of Notre Dame, USA Masaki Suwa, Chukyo University, Japan Barbara Tversky, Stanford University, USA Yvonne Waern, Linkoeping University, Sweden 19-Sep-2001 17:19:39 -0300,1198;000000000001-00000017 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8JHA8P14635 for categories-list; Wed, 19 Sep 2001 14:10:08 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Tue, 18 Sep 2001 22:29:09 -0400 (EDT) From: Susan Niefield To: Subject: categories: Union College Conference Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk We hope this message finds you well, and that your family and friends are okay after last week's tragedies. We are planning to go ahead with the Union College conference on the weekend of September 29-30. A complete schedule for the conference, including talks in the parallel sessions, is now availabe at our website www.math.union.edu/~niefiels/01Conference/ If you are planning to attend, but have not yet registered or contacted us, please do so by Monday, September 24th, so that we will be able to make arrangements for the conference banquet. Thanks. 20-Sep-2001 19:26:16 -0300,1388;000000000000-00000018 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8KJSKO31759 for categories-list; Thu, 20 Sep 2001 16:28:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <20010917184755.49751.qmail@web12204.mail.yahoo.com> Date: Mon, 17 Sep 2001 11:47:55 -0700 (PDT) From: Galchin Vasili Subject: categories: RFC Walters "Categories and Computer Science" To: categories@mta.ca MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk Hello, I am rereading Walters' book in particular the functor chapter. I am also reading Barr & Wells "Category Theory for Computing Science" (erd edition) ... in particular chapter 4 on diagrams, sketches, etc. In Walters' functor chapter, I am wondering whether Example 13 is totally correct. It doesn't seem to me that "A" is a graph and what is called a functor is really a graph morphism or to put it another way, Example 13 should be couched in terms of a (formal!!) diagram of shape "A". I know that somebody will respond and say that "A" is really a category with implicit identity arrows. However, my retort would be that "A" is intended to be a graph (without composition). What do others think? Regards, Bill Halchin 20-Sep-2001 19:27:30 -0300,1707;000000000000-00000019 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8KJhsO27981 for categories-list; Thu, 20 Sep 2001 16:43:54 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Thu, 20 Sep 2001 15:25:13 +0100 From: Jules Bean To: categories@mta.ca Subject: categories: Tangle, Braid... related category? Message-ID: <20010920152513.A28944@blueberry.jellybean.co.uk> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i Sender: cat-dist@mta.ca Precedence: bulk There's a category Braid, or Brd, whose objects are the natural numbers and morphisms "n parallel pieces of string twisted around each other". And a related one Tng where the objects distinguish between 'string going in' and 'string going out', and strings are allowed to double back on themselves. Related to these two these is a category whose objects are again the natural numbers, and whose morphisms are pieces of string which are allowed to split into multiple strands, and join together into single strands, such as the following morphism 3 --> 2: * * * \ / / | /\ \ / | \/ | * * (excuse the crude drawing which will only look OK if you have a monospaced font). There are various ways this category could be formulated (are the strings allowed to cross each other? are they allowed to double back? etc), but my question is: has anything been written about it? Does it have a name? Does it remind anyone of another category which has been studied? Yours, Jules Bean 20-Sep-2001 20:06:37 -0300,6821;000000000001-0000001a Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8KJqK007706 for categories-list; Thu, 20 Sep 2001 16:52:20 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Mon, 17 Sep 2001 21:11:34 +0200 (MET DST) From: Etaps 2002 Message-Id: <200109171911.f8HJBYG15319@cougourde.imag.fr> To: categories@mta.ca Subject: categories: CFP: ETAPS 2002 Sender: cat-dist@mta.ca Precedence: bulk Please apologize if you receive multiple copies of this message. ********************************************************** *** ETAPS 2002 *** *** APRIL, 6-14, 2002 *** *** GRENOBLE, FRANCE *** ********************************************************** The European Joint Conferences on Theory and Practice of Software ETAPS is a loose and open confederation of conferences and other events that has become the primary European forum for academic and industrial researchers working on topics relating to Software Science. ****************************** * http://www-etaps.imag.fr/ * ****************************** CALL FOR SUBMISSIONS ----------------------------------------------------------------------- 5 Conferences - 13 Satellite Events - Tutorials - Tool Demonstrations ----------------------------------------------------------------------- Conferences ----------------------------------------------------------------------- CC 2001: International Conference on Compiler Construction Chair: Nigel Horspool http://www.csr.UVic.CA/cc2002/ ESOP 2001, European Symposium On Programming Chair: Daniel Le Metayer FASE 2001, Fundamental Approaches to Software Engineering Chairs: Ralf-Detlef Kutsche and Herbert Weber http://www.cis.cs.tu-berlin.de/~fase2002/index_general.html FOSSACS 2001 Foundations of Software Science and Computation Structures Chair: Mogens Nielsen http://www.brics.dk/fossacs02/ TACAS 2001, Tools and Algorithms for the Construction and Analysis of Systems Chairs: Perdita Stevens and Joost-Pieter Katoen Tool chair: Hubert Garavel http://www.dcs.ed.ac.uk/tacas2002/ Satellite Events ----------------------------------------------------------------------- ACL2: Third Workshop on the ACL2 Theorem Prover and its Applications Contact: Matt Kaufmann, matt.kaufmann@amd.com http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/ AGT: APPLIGRAPH Workshop on Applied Graph Transformation Contact: Hans-Jvrg Kreowski, kreo@informatik.uni-bremen.de http://www.informatik.uni-bremen.de/theorie/AGT2002 CMCS: Coalgebraic Methods in Computer Science Contact: Larry Moss, University of Indiana, lsm@cs.indiana.edu http://www.cs.indiana.edu/cmcs COCV: Compiler Optimization Meets Compiler Verification Contact: Jens Knoop, knoop@ls5.cs.uni-dortmund.de http://sunshine.cs.uni-dortmund.de/~knoop/cocv02.html DCC: Designing Correct Circuits Contact: Mary Sheeran, ms@cs.chalmers.se http://www.cs.chalmers.se/~ms/DCC02/ INT: Second Workshop on Integration of Specification Techniques for Applications in Engineering Contact: Martin Gro_e-Rhode, mgr@cs.tu-berlin.de http://tfs.cs.tu-berlin.de/~mgr/int02/ LDTA: Second Workshop on Language Descriptions, Tools and Applications Contact: Marjan Mernik, marjan.mernik@uni-mb.si http://www.cwi.nl/conferences/LDTA2002/ SC: Software Composition Contact: Elke Pulverm|ller, pulvermueller@acm.org http://i44www.info.uni-karlsruhe.de/~pulvermu/workshops/SC2002 SFEDL: Semantic Foundations of Engineering Design Languages Contact: Gerald L|ttgen, g.luettgen@dcs.shef.ac.uk http://www.dcs.shef.ac.uk/~sfedl SLAP: Synchronous Languages, Applications, and Programming Contact: Florence Maraninchi, Florence.Maraninchi@imag.fr http://www.inrialpes.fr/bip/people/girault/Publications/Slap02 SPIN: 9th International SPIN Workshop on Model Checking of Software Contact: Stefan Leue, spin2002@informatik.uni-freiburg.de http://tele.informatik.uni-freiburg.de/spin2002 TPTS: Theory and Practice of Timed Systems Contact: Oded Maler, Oded.Maler@imag.fr http://www-verimag.imag.fr/~maler/TPTS.html VISS: Validation and Implementation of Scenario-based Specifications Contact: Anca Muscholl, muscholl@liafa.jussieu.fr http://www.liafa.jussieu.fr/~anca/VISS02.html Tutorials ----------------------------------------------------------------------- Proposals for half-day or full-day tutorials related to ETAPS 2001 are invited. Tutorial proposals will be evaluated on the basis of their assessed benefit for prospective participants to ETAPS 2001. Contact: Saddek Bensalem, Verimag, Saddek.Bensalem@imag.fr Tool Demonstrations ----------------------------------------------------------------------- Demonstrations of tools presenting advances on the state of the art are invited. Submissions in this category should present tools having a clear connection to one of the main ETAPS conferences, possibly complementing a paper submitted separately. Contact: Peter D. Mosses, etaps2002-demo@brics.dk ----------------------------------------------------------------------- INVITED SPEAKERS ----------------------------------------------------------------------- Ed Clarke, Carnegy Mellon University, USA (Spin workshop) Bruno Courcelle, LaBRI, Bordeaux, France Patrick Cousot, ENS Paris, France John Daniels, Syntropy Limited, London, UK Daniel Jackson, Massachusetts Institute of Technology, USA Michael Lowry, NASA Ames Research Center, USA Greg Morrisett, Cornell University, USA Mary Shaw, Carnegy Mellon University, USA ----------------------------------------------------------------------- IMPORTANT DATES ----------------------------------------------------------------------- October 19, 2001: Submissions Deadline for the Main Conferences, Demos and Tutorials December 14, 2001: Notification of Acceptance/Rejection January 18 2002: Camera-ready Version Due April 8-12, 2002: ETAPS main Conferences in GRENOBLE April 6-14, 2001: Satellite Events ----------------------------------------------------------------------- ----------- you received this e-mail via the individual or collective address categories@mta.ca to unsubscribe from ETAPS list: contact etaps02@ormelune.imag.fr 20-Sep-2001 21:01:16 -0300,27292;000000000000-0000001b Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8KJZxR15156 for categories-list; Thu, 20 Sep 2001 16:35:59 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 X-Sender: kreo@pop.informatik.uni-bremen.de (Unverified) Message-Id: Date: Wed, 19 Sep 2001 12:59:15 +0100 To: categories@mta.ca From: Kreowski Subject: categories: ICGT 2002 first announcement Content-Type: text/plain; charset="iso-8859-1" ; format="flowed" Sender: cat-dist@mta.ca Precedence: bulk Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f8KJZxR15156 Dear Colleague, Please find below the first announcement of the 1st International Conference on Graph Transformation (ICGT 2002) as a simple text. Slightly more fancy versions can be found under http://www.informatik.uni-bremen.de/theorie/icgtfa.pdf http://www.informatik.uni-bremen.de/theorie/icgtflyer.pdf The latter may be printed on a single sheet of paper (front and back) and provides a 4-page flyer if folded in the middle. Please visit also the ICGT 2002 website for more detailed information: http://www.lsi.upc.es/icgt2002 . With kind regards, Andrea Corradini and Hans-Joerg Kreowski xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Please apologize if you receive multiple copies of this message. FIRST ANNOUNCEMENT ICGT 2002 1st International Conference on Graph Transformation Barcelona (Spain), October 7-12, 2002 The first international conference on graph transformation ICGT 2002 including several satellite events will be held in Barcelona in the second week of October 2002. It follows a series of six international workshops on graph transformation with applications in computer science held from 1978 to 1998 in Europe and the USA. The conference takes place under the auspices of EATCS, EASST, and IFIP WG 1.3. The proceedings of ICGT will be published by Springer-Verlag in Lecture Notes in Computer Science. Scope. Graphical structures of various kinds (like graphs, diagrams, visual sentences and others) are very useful to describe complex structures and systems in a direct and intuitive way. These structures are often augmented by formalisms which add to the static description a further dimension allowing for the modelling of the evolution of systems via any kind of transformation of such graphical structures. The field of Graph Transformation is concerned with the theory, applications and implementation issues of all these formalisms. The theory is strongly related to areas such as graph theory and graph algorithms, formal language and parsing theory, theory of concurrency and distributed systems, formal specification and verification, logic and semantics. The application areas include all those fields of Computer Science, Information Processing, Engineering and Natural Sciences where static and dynamic modeling by graphical structures and graph transformations, respectively, play an important role. In many of these areas tools based on graph transformation technology have been implemented and used. Topics of interest include, but are not limited to the following. On the more theoretical side: - General models of graph transformation - Node-, edge-, and hyperedge replacement graph grammars - Concurrency, distribution, and formal semantics - Term graph rewriting - Network computing - High-level replacement systems - Hierarchical graphs and decompositions of graphs - Logic expression of graph transformation properties - Graph theoretical properties of graph languages - Geometrical and topological aspects of graph transformation - Automata on graphs and parsing of graph languages - Analysis of graph transformation systems - Structuring and modularization concepts - Semantics of UML and other visual modelling techniques On the more applied side: - Specification languages - Implementation of programming languages - Design of visual programming environments - Massively parallel computing - Software engineering and modular systems - Development of meta CASE tools - Software architecture - Information security - Visual languages - Actor systems and Petri nets - Rule- and knowledge-based systems - Developmental systems - Pattern generation and picture processing - Pattern matching - Tool support - Graph exchange formats - Layout algorithms Invited speakers. Carlo Ghezzi (Milano, Italy) David Harel (Rehovot, Israel) Robin Milner (Cambridge, UK) Program committee. Michel Bauderon (Bordeaux, France), Paolo Bottoni (Rome, Italy), Andrea Corradini (co-chair; Pisa, Italy), Hartmut Ehrig (Berlin, Germany), Gregor Engels (Paderborn, Germany), Reiko Heckel (Paderborn, Germany), Dirk Janssens (Antwerp, Belgium), Hans-Jörg Kreowski (co-chair; Bremen, Germany), Ugo Montanari (Pisa, Italy), Manfred Nagl (Aachen, Germany), Fernando Orejas (Barcelona, Spain), Francesco Parisi-Presicce (Rome, Italy), Mauro Pezzé (Milano, Italy), John Pfaltz (Charlottesville, Virginia, USA), Rinus Plasmeijer (Nijmegen, The Netherlands), Detlef Plump (York, Great Britain), Azriel Rosenfeld (Maryland, USA), Grzegorz Rozenberg (Leiden, The Netherlands), Andy Schürr (Munich, Germany), Gabriele Taentzer (Berlin, Germany), Gabriel Valiente (Barcelona, Spain) Important dates. Submission of papers: April 1, 2002 Notification of acceptance: June 1, 2002 Final version due: June 20, 2002 Main conference: October 8-11, 2002 Conference including satellite events: October 7-12, 2002 General Organizing Committee. Andrea Corradini (Pisa, Italy), Hartmut Ehrig (chair; Berlin, Germany), Hans-Jörg Kreowski (Bremen, Germany), Fernando Orejas (Barcelona, Spain), Grzegorz Rozenberg (Leiden, The Netherlands) Local Organizing Committee. Nikos Mylonakis, Fernando Orejas (chair), Elvira Pino, Gabriel Valiente Steering committee. Michel Bauderon (Bordeaux, France), Andrea Corradini (Pisa, Italy), Hartmut Ehrig (chair; Berlin, Germany), Gregor Engels (Paderborn, Germany), Dirk Janssens (Antwerp, Belgium), Hans-Jörg Kreowski (Bremen, Germany), Ugo Montanari (Pisa, Italy), Manfred Nagl (Aachen, Germany), Francesco Parisi-Presicce (Rome, Italy), John Pfaltz (Charlottesville, Virginia, USA), Rinus Plasmeijer (Nijmegen, The Netherlands), Azriel Rosenfeld (Maryland, USA), Grzegorz Rozenberg (Leiden, The Netherlands) More details concerning ICGT 2002 including the main conference, satellite events, submission of papers, local information on the conference site, and travel information can be found on the website of ICGT 2002, http://www.lsi.upc.es/icgt2002 . For further information, you may contact also Andrea Corradini (andrea@di.unipi.it), Hans-Joerg Kreowski (kreo@informatik.uni-bremen.de) or Fernando Orejas (orejas@lsi.upc.es). Conference address. ICGT 2002 Fernando Orejas Universitat Politčcnica de Catalunya Departament de Llenguatges i Sistemes Informŕtics Campus Nord - Edif. C6 08034 Barcelona, Spain Tel: +93 401 7018 Fax: +93 401 7014 Satellite events. GRA-TRA TUTORIAL Tutorial on Foundations and Applications of Graph Transformation Date: Oct. 8 (morning) Organizers, contact and further information: Luciano Baresi (baresi@elet.polimi.it), Reiko Heckel (reiko@upb.de) http://www.upb.de/cs/ag-engels/Conferences/ICGT02/Tutorial DNA GRA-TRA 2002 Tutorial on DNA Computing and Graph Transformation Date: Oct. 7 Organizers: Tero Harju (Turku, Finland), Grzegorz Rozenberg (Leiden, The Netherlands) Contact and further information: rozenber@liacs.nl TERMGRAPH 2002 International Workshop on Term Graph Rewriting Date: Oct. 7 Organizer, contact and further information: Detlef Plump (det@cs.york.ac.uk) http://www.cs.york.ac.uk/~det/Termgraph_2002/cfp.html GraBaTs 2002 International Workshop on Graph-Based Tools Date: Oct. 7 - 8 (lunch) Organizers: Tom Mens (Brussels, Belgium), Andy Schürr (Munich, Germany), Gabriele Taentzer (Berlin, Germany) Contact and further information: gabi@cs.tu-berlin.de, http://tfs.cs.tu-berlin.de/grabats . GT-VMT 2002 International Workshop on Graph Transformation and Visual Modeling Techniques Date: Oct. 11 (lunch) - Oct. 12 Organizers: Paolo Bottoni (Rome, Italy), Mark Minas (Erlangen, Germany) Contact and further information: bottoni@dsi.uniroma1.it, mark.minas@informatik.uni-erlangen.de http://www2.cs.fau.de/GTVMT02/ . SOFTWARE EVOLUTION Workshop on software evolution through transformations: Towards uniform support throughout the software life-cycle Date: Oct. 11 (lunch) - Oct. 12 (lunch) Organizers: Reiko Heckel (Paderborn, Germany), Tom Mens (Brussels, Belgium), Michel Wermelinger (Lisbon, Portugal) Contact and further information: reiko@upb.de, http://www.upb.de/cs/ag-engels/Conferences/ICGT02/FSWE . LOGIC, GRAPH TRANSFORMATIONS AND DISCRETE STRUCTURES Workshop with invited lectures and short contributions Date: Oct. 11 (lunch) - Oct. 12 Organizers: Bruno Courcelle (Bordeaux, France), Pascal Weil (Bordeaux, France) Contact and further information: pascal.weil@labri.fr, http://dept-info.labri.fr/~weil/LGTDD-Barcelona2002 . xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx -- --Content-Type: text/html; charsetContent-Transfer-Encoding: quoted-printable ICGT 2002 first announcement
Dear Colleague,

Please find below the first announcement of the 1st International Conference
on Graph Transformation (ICGT 2002) as a simple text. Slightly more fancy
versions can be found under

http://www.informatik.uni-bremen.de/theorie/icgtfa.pdf

http://www.informatik.uni-bremen.de/theorie/icgtflyer.pdf


The latter may be printed on a single sheet of paper (front and back) and
provides a 4-page flyer if folded in the middle.

Please visit also the ICGT 2002 website for more detailed information:

              http://www.lsi.upc.es/icgt2002 .

With kind regards, Andrea Corradini and Hans-Joerg Kreowski

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

 Please apologize if you receive multiple copies of this message.


                 FIRST ANNOUNCEMENT


              ICGT 2002

            1st International Conference 
               on Graph Transformation 

           
             Barcelona (Spain), October 7-12, 2002


The first international conference on graph transformation ICGT 2002
including several satellite events will be held in Barcelona in the
second week of October 2002. It follows a series of six international
workshops on graph transformation with applications in computer science
held from 1978 to 1998 in Europe and the USA. The conference takes place
under the auspices of EATCS, EASST, and IFIP WG 1.3. The proceedings of
ICGT will be published by Springer-Verlag in Lecture Notes in Computer
Science.                                                                         
                                                                           

Scope.  Graphical structures of various kinds (like graphs, diagrams,
visual sentences and others) are very useful to describe complex structures
and systems in a direct and intuitive way. These structures are often
augmented by formalisms which add to the static description a further
dimension allowing for the modelling of the evolution of systems via any
kind of transformation of such graphical structures. The field of Graph
Transformation is concerned with the theory, applications and implementation
issues of all these formalisms.

The theory is strongly related to areas such as graph theory and graph
algorithms, formal language and parsing theory, theory of concurrency and
distributed systems, formal specification and verification, logic and
semantics. The application areas include all those fields of Computer
Science, Information Processing, Engineering and Natural Sciences where
static and dynamic modeling by graphical structures and graph transformations,
respectively, play an important role. In many of these areas tools based
on graph transformation technology have been implemented and used.


Topics of interest include, but are not limited to the following.

On the more theoretical side:

- General models of graph transformation
- Node-, edge-, and hyperedge replacement graph grammars
- Concurrency, distribution, and formal semantics
- Term graph rewriting
- Network computing
- High-level replacement systems
- Hierarchical graphs and decompositions of graphs
- Logic expression of graph transformation properties
- Graph theoretical properties of graph languages
- Geometrical and topological aspects of graph transformation
- Automata on graphs and parsing of graph languages
- Analysis of graph transformation systems
- Structuring and modularization concepts
- Semantics of UML and other visual modelling techniques

On the more applied side:
                                                                                       - Specification languages
- Implementation of programming languages
- Design of visual programming environments
- Massively parallel computing
- Software engineering and modular systems
- Development of meta CASE tools
- Software architecture
- Information security
- Visual languages
- Actor systems and Petri nets
- Rule- and knowledge-based systems
- Developmental systems
- Pattern generation and picture processing
- Pattern matching
- Tool support
- Graph exchange formats
- Layout algorithms
        
                                                                  
Invited speakers.
          
   Carlo Ghezzi (Milano, Italy)
   David Harel (Rehovot, Israel)
   Robin Milner (Cambridge, UK)

 
Program committee. Michel Bauderon (Bordeaux, France), Paolo Bottoni
(Rome, Italy), Andrea Corradini (co-chair; Pisa, Italy), Hartmut Ehrig
(Berlin, Germany), Gregor Engels (Paderborn, Germany), Reiko Heckel
(Paderborn, Germany), Dirk Janssens (Antwerp, Belgium), Hans-Jörg Kreowski
(co-chair; Bremen, Germany), Ugo Montanari (Pisa, Italy), Manfred Nagl
(Aachen, Germany), Fernando Orejas (Barcelona, Spain), Francesco
Parisi-Presicce (Rome, Italy), Mauro Pezzé (Milano, Italy), John Pfaltz
(Charlottesville, Virginia, USA), Rinus Plasmeijer (Nijmegen, The
Netherlands), Detlef Plump (York, Great Britain), Azriel Rosenfeld
(Maryland, USA), Grzegorz Rozenberg (Leiden, The Netherlands), Andy
Schürr (Munich, Germany), Gabriele Taentzer (Berlin, Germany),
Gabriel Valiente (Barcelona, Spain)


Important dates.
       
   Submission of papers:                              April 1, 2002
   Notification of acceptance:                         June 1, 2002
   Final version due:                                 June 20, 2002
   Main conference:                              October 8-11, 2002
   Conference including satellite events:        October 7-12, 2002
         
                                                                  
General Organizing Committee.
          
Andrea Corradini (Pisa, Italy), Hartmut Ehrig (chair; Berlin, Germany),
Hans-Jörg Kreowski (Bremen, Germany), Fernando Orejas (Barcelona, Spain),
Grzegorz Rozenberg (Leiden, The Netherlands)


Local Organizing Committee.
          
Nikos Mylonakis, Fernando Orejas (chair), Elvira Pino, Gabriel Valiente


Steering committee. Michel Bauderon (Bordeaux, France), Andrea Corradini
(Pisa, Italy), Hartmut Ehrig (chair; Berlin, Germany), Gregor Engels
(Paderborn, Germany), Dirk Janssens (Antwerp, Belgium), Hans-Jörg
Kreowski (Bremen, Germany), Ugo Montanari (Pisa, Italy), Manfred Nagl
(Aachen, Germany), Francesco Parisi-Presicce (Rome, Italy), John Pfaltz
(Charlottesville, Virginia, USA), Rinus Plasmeijer (Nijmegen, The
Netherlands), Azriel Rosenfeld (Maryland, USA), Grzegorz Rozenberg
(Leiden, The Netherlands)


More details concerning ICGT 2002 including the main conference, satellite
events, submission of papers, local information on the conference site, and
travel information can be found on the website of ICGT 2002,

                    http://www.lsi.upc.es/icgt2002 .

For further information, you may contact also Andrea Corradini
(andrea@di.unipi.it), Hans-Joerg Kreowski (kreo@informatik.uni-bremen.de)
or Fernando Orejas (orejas@lsi.upc.es).

Conference address.

   ICGT 2002
   Fernando Orejas
   Universitat Politčcnica de Catalunya
   Departament de Llenguatges i Sistemes Informŕtics
   Campus Nord - Edif. C6
   08034 Barcelona, Spain
   Tel: +93 401 7018
   Fax: +93 401 7014


Satellite events.

GRA-TRA TUTORIAL
Tutorial on Foundations and Applications of Graph Transformation
Date:  Oct. 8 (morning)
Organizers, contact and further information:
Luciano Baresi (baresi@elet.polimi.it), Reiko Heckel (reiko@upb.de)
http://www.upb.de/cs/ag-engels/Conferences/ICGT02/Tutorial

DNA  GRA-TRA 2002
Tutorial on DNA Computing and Graph Transformation
Date:  Oct. 7
Organizers:
Tero Harju (Turku, Finland), Grzegorz Rozenberg (Leiden, The Netherlands)
Contact and further information: rozenber@liacs.nl

TERMGRAPH 2002
International Workshop on Term Graph Rewriting
Date: Oct. 7
Organizer, contact and further information:
Detlef Plump (det@cs.york.ac.uk)
http://www.cs.york.ac.uk/~det/Termgraph_2002/cfp.html

 
GraBaTs 2002
International Workshop on Graph-Based Tools
Date: Oct. 7 - 8 (lunch)
Organizers:
Tom Mens (Brussels, Belgium), Andy Schürr (Munich, Germany),
Gabriele Taentzer (Berlin, Germany)
Contact and further information:
gabi@cs.tu-berlin.de, http://tfs.cs.tu-berlin.de/grabats .

GT-VMT 2002
International Workshop on Graph Transformation and Visual Modeling Techniques
Date: Oct. 11 (lunch) - Oct. 12
Organizers:
Paolo Bottoni (Rome, Italy), Mark Minas (Erlangen, Germany)
Contact and further information:
bottoni@dsi.uniroma1.it, mark.minas@informatik.uni-erlangen.de
http://www2.cs.fau.de/GTVMT02/ .

SOFTWARE EVOLUTION
Workshop on software evolution through transformations:
Towards uniform support throughout the software life-cycle
Date: Oct. 11 (lunch) - Oct. 12 (lunch)
Organizers:
Reiko Heckel (Paderborn, Germany), Tom Mens (Brussels, Belgium),
Michel Wermelinger (Lisbon, Portugal)
Contact and further information:
reiko@upb.de, http://www.upb.de/cs/ag-engels/Conferences/ICGT02/FSWE .

LOGIC, GRAPH TRANSFORMATIONS AND DISCRETE STRUCTURES
Workshop with invited lectures and short contributions
Date: Oct. 11 (lunch) - Oct.  12
Organizers:
Bruno Courcelle (Bordeaux, France), Pascal Weil (Bordeaux, France)
Contact and further information:
pascal.weil@labri.fr, http://dept-info.labri.fr/~weil/LGTDD-Barcelona2002 .

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-- 21-Sep-2001 17:50:55 -0300,2454;000000000001-0000001c Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8LH7Hi27176 for categories-list; Fri, 21 Sep 2001 14:07:17 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: Re: Tangle, Braid... related category? To: categories@mta.ca Date: Thu, 20 Sep 2001 21:43:40 +0100 (BST) X-Mailer: ELM [version 2.5 PL5] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: From: Tom Leinster X-Scanner: exiscan *15kAfa-0000nm-00*mmmpkThzkHA* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk Jules Bean wrote: [...] > Related to these two these is a category whose objects are again the > natural numbers, and whose morphisms are pieces of string which are > allowed to split into multiple strands, and join together into single > strands, such as the following morphism 3 --> 2: > > * * * > \ / / > | /\ > \ / | > \/ | > * * > > (excuse the crude drawing which will only look OK if you have a > monospaced font). > > There are various ways this category could be formulated (are the > strings allowed to cross each other? are they allowed to double back? > etc), but my question is: has anything been written about it? Does it > have a name? Does it remind anyone of another category which has been > studied? I don't know if it has a name, but it's the free strict monoidal category containing a bimonoid. By a bimonoid I mean an object which has both the structure of a monoid and a comonoid, with the two structures compatible with each other. So multiplication looks like * * \ / | * and comultiplication is the other way up. The unit looks like | * (a string coming out of nowhere); if you find this unpleasant then don't have units or counits, in other words, take the free strict monoidal category containing a "bisemigroup" (now there's a daft name). Crossings could be allowed by introducing (co)commutativity, and doubling back by introducing duality (or nondegenerate bilinear forms, in the world of vector spaces). Similarly, Brd is the free braided strict monoidal category on one object, and Tng (tangles) has a similar description (doesn't it?). Tom 21-Sep-2001 17:54:59 -0300,3285;000000000001-0000001d Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8LHEhq02821 for categories-list; Fri, 21 Sep 2001 14:14:43 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <3.0.5.32.20010921101332.00826520@TESLA.open.ac.uk> X-Sender: sjv22@TESLA.open.ac.uk X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.5 (32) Date: Fri, 21 Sep 2001 10:13:32 +0100 To: categories@mta.ca From: S Vickers Subject: categories: Re: RFC Walters "Categories and Computer Science" In-Reply-To: <20010917184755.49751.qmail@web12204.mail.yahoo.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk >Hello, > > I am rereading Walters' book in particular the >functor chapter. I am also reading Barr & Wells >"Category Theory for Computing Science" (erd edition) >... in particular chapter 4 on diagrams, sketches, >etc. In Walters' functor chapter, I am wondering >whether Example 13 is totally correct. It doesn't >seem to me that "A" is a graph and what is called >a functor is really a graph morphism or to put it >another way, Example 13 should be couched in terms >of a (formal!!) diagram of shape "A". I know that >somebody will respond and say that "A" is really >a category with implicit identity arrows. However, >my retort would be that "A" is intended to be a >graph (without composition). What do others think? > >Regards, Bill Halchin > > I haven't got either books in front of me at the moment, so I hope I'm not going off on a tangent. However, there is a definite choice of approach here: Is the shape of a diagram a graph or a category? They are mathematically equivalent. If a graph-shaped diagram has shape A, then one can form the free category Path(A) over A (objects are the nodes, morphisms are chains of edges) and uniquely extend the graph morphism from A to a functor from Path(A). I guess the reason for choosing the category-shaped diagrams is that one can then apply directly all that is known about functors and natural transformations. However, that choice is not entirely benign. For a start, it seems beyond doubt that when one draws a diagram one is drawing a graph. The graph is easier to deal with mentally, and a finite graph may generate an infinite category. One particular context where I have found graph-shaped diagrams easier to handle mathematically is in cocompletion. Suppose you have a category C and want to adjoin, freely, all colimits, to give a bigger category Cocomp(C). One approach is to use diagrams as the objects of Cocomp(C), representing their colimits, and another is to use presheaves. The relationship between the two is best seen with graph-shaped diagrams, for they present presheaves in a simple way. Going to path categories just complicates everything, and covers up the simple correspondence between finitely shaped diagrams and finitely presentable presheaves (needed for finite cocompletion). This is discussed in my paper with Gillian Hill, "Presheaves as configured specifications", Formal Aspects of Computing 13 (Sep 2001) pp. 32-49. Steve Vickers. 21-Sep-2001 17:56:10 -0300,1535;000000000001-0000001e Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8LHJkM30508 for categories-list; Fri, 21 Sep 2001 14:19:46 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <20010921151800.42633.qmail@web12203.mail.yahoo.com> Date: Fri, 21 Sep 2001 08:18:00 -0700 (PDT) From: Galchin Vasili Subject: categories: Re: RFC Walters "Categories and Computer Science" To: categories@mta.ca In-Reply-To: <3.0.5.32.20010921101332.00826520@TESLA.open.ac.uk> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Sender: cat-dist@mta.ca Precedence: bulk It is a diagram of a graph and the shape is purely a graph (I.E. it would be wrong to see implicit identity morphisms in this example). I have alwasy had problems with this example. I do love the book though. Regards, Bill --- S Vickers wrote: > >Hello, > > > > I am rereading Walters' book in particular the > >functor chapter. I am also reading Barr & Wells ... > >graph (without composition). What do others think? > > > >Regards, Bill Halchin > > > I haven't got either books in front of me at the > moment, so I hope I'm not > going off on a tangent. However, there is a definite ... > This is discussed in my paper with Gillian Hill, > "Presheaves as configured > specifications", Formal Aspects of Computing 13 (Sep > 2001) pp. 32-49. > > Steve Vickers. > 21-Sep-2001 18:05:57 -0300,1334;000000000001-0000001f Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8LH9qQ31713 for categories-list; Fri, 21 Sep 2001 14:09:52 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Fri, 21 Sep 2001 08:29:26 +1000 To: categories@mta.ca Subject: categories: Re: Tangle, Braid... related category? Message-ID: <20010921082926.B779@platinum.idesign.fl.net.au> References: <20010920152513.A28944@blueberry.jellybean.co.uk> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <20010920152513.A28944@blueberry.jellybean.co.uk> User-Agent: Mutt/1.3.22i From: Duraid Madina Sender: cat-dist@mta.ca Precedence: bulk > There are various ways this category could be formulated (are the > strings allowed to cross each other? are they allowed to double back? > etc), but my question is: has anything been written about it? Does it > have a name? Does it remind anyone of another category which has been > studied? I vaguely recall these being referred to as "vines", and I think a text by Joan Birman dealt with them a little. I'm not sure as to how far these things were "categorified", though. Sorry for being so vague, Duraid 23-Sep-2001 13:22:35 -0300,2528;000000000000-00000020 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8NEaQ902696 for categories-list; Sun, 23 Sep 2001 11:36:26 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Sat, 22 Sep 2001 15:49:23 +0100 (BST) From: "Dr. P.T. Johnstone" To: categories@mta.ca Subject: categories: Re: categories or graphs? In-Reply-To: <3.0.5.32.20010921101332.00826520@TESLA.open.ac.uk> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Scanner: exiscan *15ko5q-0006qq-00*xHRGd9nuI8Q* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk On Fri, 21 Sep 2001, S Vickers wrote: > I haven't got either books in front of me at the moment, so I hope I'm not > going off on a tangent. However, there is a definite choice of approach > here: Is the shape of a diagram a graph or a category? > > They are mathematically equivalent. If a graph-shaped diagram has shape A, > then one can form the free category Path(A) over A (objects are the nodes, > morphisms are chains of edges) and uniquely extend the graph morphism from > A to a functor from Path(A). > > I guess the reason for choosing the category-shaped diagrams is that one > can then apply directly all that is known about functors and natural > transformations. > > However, that choice is not entirely benign. For a start, it seems beyond > doubt that when one draws a diagram one is drawing a graph. The graph is > easier to deal with mentally, and a finite graph may generate an infinite > category. > No, that's not the reason. Steve is right that what we actually draw and call "diagrams" are the images of graph morphisms, but we also make assertions (often without stating them explicitly) that certain parts of the diagrams commute, so that what we think of as the "shape" of a diagram is not simply a directed graph but (a presentation of) a category. For example, if I want to talk (as I often do) about properties of reflexive coequalizers in a category, I need to consider diagrams whose shape is the category generated by morphisms f: A --> B, g: A --> B and s: B --> A subject to the equations fs = gs = 1_B. If Steve is only willing to allow me to talk about diagrams whose shape is (the free category generated by) a directed graph, then I can't do this. Peter Johnstone 23-Sep-2001 13:37:39 -0300,3348;000000000000-00000021 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8NEXah26926 for categories-list; Sun, 23 Sep 2001 11:33:36 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3BAB90E5.295995B8@cogs.susx.ac.uk> Date: Fri, 21 Sep 2001 20:11:33 +0100 From: Bernhard Reus Organization: COGS, University of Sussex X-Mailer: Mozilla 4.76 [en] (X11; U; SunOS 5.7 sun4u) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: job: PhD studentship at Sussex Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Please pass on to interested students. Apologies for multiple copies. --------------------------------------------------------------------- A three year PhD studentship is available as part of the EPSRC project `Programming Logics for Denotations of Recursive Objects' at the School of Cognitive and Computing Sciences (COGS) at the University of Sussex at Brighton. The aim of this project is to develop a programming logic for an object-oriented language based on denotational semantics. Starting from some results already obtained for untyped languages the main task will be to derive and study reasoning principles in a _typed_ setting. LCF (Logic of Computable Functions), developped in the seventies, acts somehow as our role model. Mechanized even by a powerful theorem prover, it supports reasoning about functional programs. We plan to follow similar objectives for the object-based paradigm. Prototypical implementations of (parts of) results using a theorem prover are not the main focus of the project, but may turn out to be fruitful during the development process. Prospective candidates should have an appropriate degree in computer science or mathematics. Some background in programming logics, domain theory or type theory are useful but not essential. The studentship will cover all fees for a three year period and a yearly maintenance grant at the standard rate (currently GBP 6800). It comes with sufficient funds to cover travel to summer schools and conferences, and possibly brief visits to other institutions. A possible starting date is January 2002, but earlier or slightly later dates can be arranged. The project student will be a member of the Foundations group at COGS. This group (see also http://www.cogs.susx.ac.uk/foundations ) shares interests in all kinds of semantical questions and runs regular internal seminars and other events. It consists currently of five members of staff (Hennessy, McCusker, Rathke, Reus, Sassone), three research fellows (Harmer, Laird, Merro) and two PhD students. The group is still growing and its manageable size is considered beneficial to the internal scientific exchange. Brighton itself is a enchanting, exciting, and extraordinary seaside city. With its cosmopolitan air, feverish nightlife, abundance of culture, and vicinity to London, it is an attractive place to live and study (more info: http://www.susx.ac.uk/central/students.shtml ). For enquiries and further details please contact Bernhard Reus at bernhard@cogs.susx.ac.uk 23-Sep-2001 13:38:30 -0300,3835;000000000000-00000022 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8NEW4V08078 for categories-list; Sun, 23 Sep 2001 11:32:04 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f From: baez@math.ucr.edu Message-Id: <200109211747.f8LHlOf27139@math-cl-n05.ucr.edu> Subject: categories: re: Tangle, Braid... related category? To: categories@mta.ca (categories) Date: Fri, 21 Sep 2001 10:47:24 -0700 (PDT) In-Reply-To: from "Tom Leinster" at Sep 20, 2001 09:43:40 PM X-Mailer: ELM [version 2.5 PL2] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Tom Leinster wrote: > Jules Bean wrote: > > Related to these two these is a category whose objects are again the > > natural numbers, and whose morphisms are pieces of string which are > > allowed to split into multiple strands, and join together into single > > strands, such as the following morphism 3 --> 2: > > > > * * * > > \ / / > > | /\ > > \ / | > > \/ | > > * * > > > > (excuse the crude drawing which will only look OK if you have a > > monospaced font). > > > > There are various ways this category could be formulated (are the > > strings allowed to cross each other? are they allowed to double back? > > etc), but my question is: has anything been written about it? Does it > > have a name? Does it remind anyone of another category which has been > > studied? > I don't know if it has a name, but it's the free strict monoidal category > containing a bimonoid. By a bimonoid I mean an object which has both the > structure of a monoid and a comonoid, with the two structures compatible with > each other. This answer is a bit more definite-sounding than the one I would give. First of all, Jules Bean leaves it quite open-ended exactly which category he is talking about. He is actually talking about a large number of interesting categories each with their own description. Secondly, the usual definition of bimonoid involves structures and laws that are not so natural from the topological viewpoint - i.e., certain morphisms are decreed to be equal even when their corresponding embedded graphs are not isotopic. Whether this is good or bad depends on what you're trying to do. But anyway: there are lots of interesting categories along these general lines! Tom has described one, and like his example they all tend to have nice universal properties - i.e. they tend to be the "free ..... category on a .....". As described here: Higher-dimensional algebra and topological quantum field theory, with James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105. Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189. the category of framed tangles in 2/3/4 dimensions is the "free monoidal/braided/symmetric category with duals on one object". We can enhance these categories to obtain various categories of embedded framed graphs by throwing in extra morphisms involving our object, which give vertices in our graph. We can also get rid of the framing or "doubling back" by eliminating various clauses buried within the phrase "with duals". I don't know of anyone who attempted to write about *all* these variations - there are just too many to handle individually, and people haven't yet tackled the general theory of such categories (though such a theory does exist). However, you can find a lot of examples treated in Yetter's book "Functorial Knot Theory", Turaev's book on "Quantum Invariants of Knots and 3-Manifolds", and the references in my papers above. 23-Sep-2001 13:41:47 -0300,3994;000000000000-00000023 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8NEZj801128 for categories-list; Sun, 23 Sep 2001 11:35:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Mime-Version: 1.0 Message-Id: In-Reply-To: References: Date: Sat, 22 Sep 2001 01:56:55 +0200 To: categories@mta.ca From: Joachim Kock Subject: categories: Re: Tangle, Braid... related category? Content-Type: text/plain; charset="iso-8859-1" ; format="flowed" X-MIME-Autoconverted: from 8bit to quoted-printable by taloa.unice.fr id BAA51127 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id f8LNv4Q16008 Sender: cat-dist@mta.ca Precedence: bulk Jules Bean: [...] > Related to these two these is a category whose objects are again the > natural numbers, and whose morphisms are pieces of string which are > allowed to split into multiple strands, and join together into single > strands, such as the following morphism 3 --> 2: > > * * * > \ / / > | /\ > \ / | > \/ | > * * > > There are various ways this category could be formulated (are the > strings allowed to cross each other? are they allowed to double back? > etc), but my question is: has anything been written about it? Does it > have a name? Does it remind anyone of another category which has been > studied? Tom Leinster: > I don't know if it has a name, but it's the free strict monoidal category > containing a bimonoid. By a bimonoid I mean an object which has both the > structure of a monoid and a comonoid, with the two structures compatible with > each other. So multiplication looks like > > * * > \ / > | > * > > and comultiplication is the other way up. The unit looks like > > | > * > > (a string coming out of nowhere); if you find this unpleasant then don't have > units or counits, in other words, take the free strict monoidal category > containing a "bisemigroup" (now there's a daft name). Crossings could be > allowed by introducing (co)commutativity, and doubling back by introducing > duality (or nondegenerate bilinear forms, in the world of vector spaces). Once you have units and counits you automatically get duality (doubling back): just compose the multiplication with the counit: * * * * \ / \/ | = * | To complement Tom's good description with some more names: With crossings (commutativity), we've got the skeleton of the category 2COB (objects: compact oriented 1-manifolds, arrows: (diffeomorphism classes of) 2-cobordisms). In the drawings, the 'particles' are then replaced by 'closed strings'; we get those 'pair-of-pants' for the (co)multiplication, and 'caps' for (co)unit. The representations of 2COB are called 2D topological quantum field theories, and the category of those is equivalent to the category of (commutative) Frobenius algebras. A detailed reference for this is @article{Abrams:tqft, author = {Lowell Abrams}, title = {Two-dimensional topological quantum field theories and Frobenius algebras}, journal = {J.~Knot Theory and its Ramifications}, volume = 5, year = 1996, pages = {569--587}, } (available on his home page, I think.) Cheers, Joachim. ---------------------------------------------------------------------- Joachim KOCK Laboratoire de Mathématiques J.A.Dieudonné Tél. +33 04.92.07.62.40 Université de Nice Sophia-Antipolis Fax +33 04.93.51.79.74 Parc Valrose - 06108 Nice cédex 2 - FRANCE Mél. kock@math.unice.fr ---------------------------------------------------------------------- 24-Sep-2001 11:36:51 -0300,1905;000000000001-00000024 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8OCYt408762 for categories-list; Mon, 24 Sep 2001 09:34:55 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Subject: categories: re: Tangle, Braid... related category? To: categories@mta.ca Date: Sun, 23 Sep 2001 21:23:54 +0100 (BST) X-Mailer: ELM [version 2.5 PL5] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-Id: From: Tom Leinster X-Scanner: exiscan *15lFn5-0007CF-00*baWp.3yP8OU* http://duncanthrax.net/exiscan/ Sender: cat-dist@mta.ca Precedence: bulk John Baez wrote, concerning categories whose morphisms look like this: * * * \ / / | /\ \ / | \/ | * * > First of all, Jules Bean leaves it quite open-ended exactly which category > he is talking about. He is actually talking about a large number of > interesting categories each with their own description. Secondly, the > usual definition of bimonoid involves structures and laws that are not > so natural from the topological viewpoint - i.e., certain morphisms are > decreed to be equal even when their corresponding embedded graphs are not > isotopic. Whether this is good or bad depends on what you're trying to > do. Agreed on all counts. It's also interesting (to me) to consider the dual diagrams, which look something like computads (depending on exactly which version of the category above you're using); this gives different geometric intuitions. There's more about this, and higher-dimensional generalizations, in Ross Street, Categorical structures, in Handbook of Algebra I, ed. M. Hazewinkel, North-Holland, 1996, pp. 529-577. Tom 26-Sep-2001 13:10:01 -0300,1644;000000000001-00000025 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8QDAxV24051 for categories-list; Wed, 26 Sep 2001 10:10:59 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-Id: <3.0.5.32.20010924101929.0082b100@TESLA.open.ac.uk> X-Sender: sjv22@TESLA.open.ac.uk X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.5 (32) Date: Mon, 24 Sep 2001 10:19:29 +0100 To: categories@mta.ca From: S Vickers Subject: categories: Re: categories or graphs? In-Reply-To: References: <3.0.5.32.20010921101332.00826520@TESLA.open.ac.uk> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: cat-dist@mta.ca Precedence: bulk Peter is quite right. I was mistaken in saying graph shape and category shape are mathematically equivalent. Category shape for diagrams has graph shape plus the commutativities, which graph shape on its own does not capture. His justification for considering category shape is much more profound than the ones I mentioned. Nonetheless, when verifying the conditions for cones/cocones, or for limits/colimits, the commutativities make no difference and it suffices to check on a generating graph. Thus it is worth bearing in mind that in such contexts one might correctly and more simply just use graph shape, as Gillian and I did in "Presheaves as configured specifications". (For those interested it's on the web via my home page at http://mcs.open.ac.uk/sjv22 .) Steve Vickers. 26-Sep-2001 13:27:29 -0300,2418;000000000000-00000026 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8QDAbg16715 for categories-list; Wed, 26 Sep 2001 10:10:37 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: rags owned process doing -bs Date: Mon, 24 Sep 2001 00:32:25 -0400 (EDT) From: "Robert A.G. Seely" To: Categories List Subject: categories: Linear Monads (Was Re: Tangle, Braid... related category?) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk > Jules Bean wrote: > Related to these two these is a category whose objects are again the > natural numbers, and whose morphisms are pieces of string which are > allowed to split into multiple strands, and join together into single > strands, such as the following morphism 3 --> 2: > > * * * > \ / / > | /\ > \ / | > \/ | > * * As Tom Leinster, Joachim Kock, and John Baez point out, there are a number of studies of such structures. But for a coherent general perspective, I would also point out that this is what we (Robin Cockett, J"urgen Koslowski, and Robert Seely) call a "linear monad" in a linear bicategory ("Introduction to Linear Bicategories", Math Struct in Comp Sci 10 (2000) 165--203, also available from my web site, url as given below). The general theory is worked out in section 4 of that paper. A linear bicategory may be thought of as a bicategory with two (usually distinct) horizontal composition operations (we think of them as tensors). In figures such as above, we can imagine one tensor as "tieing together" the top wires, and the other for the bottom wires. Monads and comonads may be defined in this setting, and a linear monad is a pair consisting of a monad and a comonad which are "compatible" with one another, each of which acts (or coacts, as appropriate) upon the other. As we point out in the paper, these are a natural generalization of Frobenius algebras, to pick up Joachim Kock's reference. - all the best, Robert (Seely) ================== R.A.G. Seely 26-Sep-2001 13:48:45 -0300,4134;000000000001-00000027 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8QDC1S27565 for categories-list; Wed, 26 Sep 2001 10:12:01 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Message-ID: <3BAF3D0F.8AEFAE6C@bangor.ac.uk> Date: Mon, 24 Sep 2001 15:02:55 +0100 From: Ronnie Brown X-Mailer: Mozilla 4.77 [en] (Win98; U) X-Accept-Language: en MIME-Version: 1.0 To: categories@mta.ca Subject: categories: Re: categories or graphs? References: Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk It may be helpful to remark that in Ronald Brown and Anne Heyworth, `Using rewriting systems to compute left Kan extensions and induced actions of categories', J. Symbolic Computation 29 (2000) 5-31. we introduce the notion of a \textbf{Kan extension presentation}. This is a quintuple $\mathcal{P}:=kan\lan \Gamma|\Delta|RelB|X|F \ran$ where \begin{enumerate}[i)] \item $\Gamma$ and $\Delta$ are graphs, \item $cat\lan \Delta | RelB \ran$ is a category presentation, \item $X: \Gamma \to U \sets$ is a graph morphism, \item $F: \Gamma \to U P\Delta$ is a graph morphism. \end{enumerate} The idea is analogous to a presentation of a group, where one gives a hopefully finite amount of information in order to compute, in some sense and in some cases, the group or in this case a Kan extension. Ronnie Brown "Dr. P.T. Johnstone" wrote: > On Fri, 21 Sep 2001, S Vickers wrote: > > > I haven't got either books in front of me at the moment, so I hope I'm not > > going off on a tangent. However, there is a definite choice of approach > > here: Is the shape of a diagram a graph or a category? > > > > They are mathematically equivalent. If a graph-shaped diagram has shape A, > > then one can form the free category Path(A) over A (objects are the nodes, > > morphisms are chains of edges) and uniquely extend the graph morphism from > > A to a functor from Path(A). > > > > I guess the reason for choosing the category-shaped diagrams is that one > > can then apply directly all that is known about functors and natural > > transformations. > > > > However, that choice is not entirely benign. For a start, it seems beyond > > doubt that when one draws a diagram one is drawing a graph. The graph is > > easier to deal with mentally, and a finite graph may generate an infinite > > category. > > > No, that's not the reason. Steve is right that what we actually draw > and call "diagrams" are the images of graph morphisms, but we also > make assertions (often without stating them explicitly) that certain > parts of the diagrams commute, so that what we think of as the > "shape" of a diagram is not simply a directed graph but (a presentation > of) a category. For example, if I want to talk (as I often do) about > properties of reflexive coequalizers in a category, I need to > consider diagrams whose shape is the category generated by morphisms > f: A --> B, g: A --> B and s: B --> A subject to the equations > fs = gs = 1_B. If Steve is only willing to allow me to talk about > diagrams whose shape is (the free category generated by) a directed > graph, then I can't do this. > > Peter Johnstone -- Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Raising Public Awareness of Mathematics CDRom Version 1.1 http://www.bangor.ac.uk/~mas010/CDadvert.html Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/ 26-Sep-2001 16:29:14 -0300,968;000000000000-00000028 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8QGmYT14505 for categories-list; Wed, 26 Sep 2001 13:48:34 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f To: categories@mta.ca Subject: categories: Re: categories or graphs? Message-Id: From: Paul Taylor Date: Wed, 26 Sep 2001 16:53:19 +0100 X-Ident: pt Sender: cat-dist@mta.ca Precedence: bulk Diagrams may sometimes be graphs. They may sometimes be categories, but it's pretty rare to specify the identity maps in them. So surely the right definition is that they are "elementary sketches", ie category presentations, not that there is any need to generate the category from them. This is the view that I take in Section 7.3 of "Practical Foundations". http://www.dcs.qmul.ac.uk/~pt/Practical_Foundations/html/s73.html Paul 28-Sep-2001 13:14:49 -0300,4330;000000000001-00000029 Return-Path: Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f8SCg7l02034 for categories-list; Fri, 28 Sep 2001 09:42:07 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Date: Wed, 26 Sep 2001 15:36:22 +0100 From: Jules Bean To: categories Subject: categories: re: Tangle, Braid... related category? Message-ID: <20010926153621.A8936@blueberry.jellybean.co.uk> References: <200109211747.f8LHlOf27139@math-cl-n05.ucr.edu> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.2.5i In-Reply-To: <200109211747.f8LHlOf27139@math-cl-n05.ucr.edu>; from baez@math.ucr.edu on Fri, Sep 21, 2001 at 10:47:24AM -0700 Sender: cat-dist@mta.ca Precedence: bulk On Fri, Sep 21, 2001 at 10:47:24AM -0700, baez@math.ucr.edu wrote: > First of all, Jules Bean leaves it quite open-ended exactly which category > he is talking about. He is actually talking about a large number of > interesting categories each with their own description. Secondly, the > usual definition of bimonoid involves structures and laws that are not > so natural from the topological viewpoint - i.e., certain morphisms are > decreed to be equal even when their corresponding embedded graphs are not > isotopic. Whether this is good or bad depends on what you're trying to > do. Thank you to everyone for the wealth of helpful answers! I appreciate that my description was not 'tight': in actual fact, there is probably more than one category I'm interested in in the family. I've followed up the references to the category 2COB (as encountered in TQFT, in Abrams' paper as well as Baez + Dolan), and that is quite similar to the category I'm describing. However, it's not quite the one I have. In 2COB, the following are equivalent (Abrams labels this relation 'F') * * * * \/ |\ | | = | \| /\ | | * * * * I suppose you might call that equation X = N . The way I've implemented my category is not as a 2-mfd, but as a 1-complex, embedded 'sensibly'. There is a distinction between some points of the boundary being the 'top', and the other points of the boundary being the 'bottom'. (Which my diagrams have been assuming). And, obviously, X and N are different as one-complexes, even though they are the deformation retracts of homeomorphic 2-mfds. (Actually, the above diagram isn't even an X, it's an X-like shape with an extended vertical section; that's a different one-complex too). I have an intuitive justification for wanting these to be different, if people aren't offended by slightly silly analogies. Think of the networks (which is what I call them) as river networks. They have to flow downhill (down the page). They can join as tributaries do, or split into distributaries. Then in the 'X' all the water has possibly mixed; we can't assume it will divide the same way. In the 'N' on the other hand, all of the water which came in on the right, has definitely gone out on the right. The other helpful lead I was given was a category (sometimes) called Vine, see Lavers [Comm. Algebra 25(4) pp1257-84], or Solomon 'A Category of Concrete Monoids' at : http://www.maths.usyd.edu.au:8000/res/Algebra/Sol/1996-07.html This is closely related to what I'm trying to do, but Vine is different in two ways. Firstly, the threads only join in Vine, never split; secondly, Vine only has morphisms from n --> n, whereas my category has morphisms from n --> m for all n and m. For example, in Vine, the morphism diagram which looks like a capital 'V' is in fact a morphism from 2 --> 2, with one node at the bottom unconnected (something like 'V.'), whereas in my category it's naturally a morphism from 2 --> 1. The principle point of uncertainty is whether or not I allow the threads to cross: this corresponds to whether some underlying monoid is commutative or not. Both possibilities are interesting. Thanks again to everyone for their help. If anyone has any further pointers to a category like the one I'm describing, I'm very interested. Yours, Jules Bean 1-Oct-2001 18:40:03 -0300,2592;000000000001-0000002a From cat-dist@mta.ca Mon Oct 01 18:40:03 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 Oct 2001 18:40:03 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 15oAWY-0005jV-00 for categories-list@mta.ca; Mon, 01 Oct 2001 18:22:50 -0300 Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 28 Sep 2001 16:11:22 +0100 To: categories@mta.ca From: grandis@dima.unige.it (Marco Grandis) Subject: categories: preprint: "Ordinary and directed combinatorial homotopy,..." Sender: cat-dist@mta.ca Precedence: bulk The following paper is available in ps and ps.gz. It is about my talk at: 'Conference on Algebraic Topological Methods in Computer Science' Stanford, July 30 - August 3, 2001. 'Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency' Marco Grandis Abstract. Combinatorial homotopical tools developed in previous works, and consisting essentially of intrinsic homotopy theories for simplicial complexes and directed simplicial complexes, can be applied to explore mathematical models representing images, or directed images, or concurrent processes. An image, represented by a metric space X, can be explored at a variable resolution e > 0, by equipping it with a structure t_eX of simplicial complex depending on e; this complex can be further analysed by homotopy groups \pi^e_n(X) = \pi_n(t_eX) and homology groups H^e_n(X) = H_n(t_eX). Loosely speaking, these objects detect singularities which can be captured by an n-dimensional grid, with edges bound by e; this works equally well for continuous or discrete regions of euclidean spaces. Similarly, a directed image, represented by an 'asymmetric metric space', produces a family of directed simplicial complexes f_eX and can be explored by the fundamental n-category of the latter. The same directed tools can be applied to mathematical models of concurrent automata, like Chu-spaces. AVAILABLE AT: ftp://www.dima.unige.it/Home/grandis/public/Cmb.App.ps ftp://www.dima.unige.it/Home/grandis/public/Cmb.App.ps.gz (18p, 260K) ***** With best regards Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ ftp://www.dima.unige.it/Home/grandis/public/ 1-Oct-2001 18:40:07 -0300,1032;000000000000-0000002b From cat-dist@mta.ca Mon Oct 01 18:40:07 2001 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 Oct 2001 18:40:07 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 15oAXF-0000NZ-00 for categories-list@mta.ca; Mon, 01 Oct 2001 18:23:33 -0300 Date: Sun, 30 Sep 2001 11:45:43 -0400 (EDT) From: Jason C Reed Reply-To: To: Subject: categories: Only two SMC structures on Cat? Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Power, A.J. and Robinson, E.P. Premonoidal categories and notions of computation (ftp://ftp.dcs.qmw.ac.uk/pub/lfp/edmundr/premoncat.ps.gz) in section 2 asserts that there is excatly one symmetric monoidal closed structure on Cat besides the cartesian one. Does anyone know [the location of] a proof? ---Jason