July 1997 - Categories - categories.org.au

Pratt's construction
by Michael Barr 30 Jul '97

30 Jul '97

Since Vaughan insists on doing these things in terms of matrices and we benighted mathematicians insist on thinking in terms of pairings, I thought it might be helpful to describe what he did in those terms. First off, he erred in writing Chu instead of chu. So it is the separated extensional part. I will describe it for chu(Set,2), since nothing much changes for other values of K except you get more dinats. I will describe three types of objects. If A = (A_1,A_2) is an object, I will say that A_1 is the set of points and A_2 the set of states and treat A_2 as a set of subsets of A_1. I will say that A is type I if there is a point in no state AND if the empty set is a state. I will say that A is of type II if there is a point in every state and if the whole of A_1 is a state. These would appear to be quite different, but they are exchanged by the non-trivial automorphism of 2, which means they have the same properties. All remaining objects will be of type III. The first observation is that the type is invariant under formation of A -o A. That is, A -o A has the same type as A. Second, if A and B are of different types, then at least one of Hom(A,B) and Hom(B,A) is empty. This implies that if there is a map A --> B, then B -o A can only be (0,1) or (0,0) (0 is the empty set). That is is either initial or a quotient of the initial object. In either case, it has at most one arrow to any other object and any diagram starting with it commutes. The result of this is that any naturality condition that involves objects of different types is automatic. Either there is no map A --> B to test or there is one and the diagram is automatically commutative. For an object of type I, there is a zero map that takes every point to the (unique!) point not in any state and takes every state to the empty state. This is natural restricted to the type I objects and there is a similar 0 map for type II's. Now there are at least four dinatural endomorphisms of the functor that takes A and B to A -o B. They are all the identity on type III objects and can be either the identity or the 0 map on type I and the same on type II. Michael

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CTCS'97 final CFP
by Eugenio Moggi 30 Jul '97

30 Jul '97

[Please look at the conference URL for more detailed information] CATEGORY THEORY AND COMPUTER SCIENCE (CTCS'97) 4-6 SEPTEMBER 1997, S. MARGHERITA LIGURE (GENOA), ITALY CONFERENCE URL: "http://www.disi.unige.it/conferences/ctcs97/" FINAL CALL FOR PARTICIPATION CTCS'97 is the 7th conference on Category Theory and Computer Science. The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory, algebra, geometry and logic. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. The proceedings will be published by Springer in the LNCS series. LOCATION. The conference will take place at Hotel Regina Elena, a 4 stars hotel with private beach, located in S. Margherita Ligure. S. Margherita is a beautiful sea resort in Liguria very close to Portofino promontory and about 30 km east of Genova. INVITED SPEAKERS - J. Baez, Univ. of California at Riverside (USA) - R. Bird, Oxford Univ. (UK) - B. Jay, Univ. of Technology Sydney (Australia) - G. Plotkin, Univ. of Edinburgh (UK) LATE REGISTRATION AND HOTEL RESERVATION. The late registration fee is 400000 It.Lire, and includes the welcome reception, coffee breaks, lunches, a copy of the proceedings. See the CONFERENCE URL for details on hotels and how to register. CONTACT INFORMATION: ctcs97(a)disi.unige.it (email), +39-10-3536699 (fax) ----------------------------------------------------------------------------- CONFERENCE PROGRAMME HOTEL REGINA ELENA Lungomare Milite Ignoto 44, 16038 S. Margherita Ligure, Italy phone: +39 (185) 287003, fax: +39 (185) 284473 WEDNESDAY, 3 September 18.00 Welcome Reception and Registration THURSDAY, 4 September 09.00 Invited Talk: Richard Bird 10.15 Coffee Break 10.40 Proof Principles for Datatypes with Iterated Recursion by Ulrich Hensel, Bart Jacobs 11.20 A Calculus for Collections and Aggregates by Kazem Lellahi, Val Tannen 12.00 When do datatypes commute? by Paul Hoogendijk, Roland Backhouse 12.40 Lunch 14.45 Invited Talk: John Baez 16.00 Coffee Break 16.30 A factorisation theorem for external derivations by Paul-Andre Mellies 17.10 Monads and Modular Term Rewriting by Christoph Lueth, Neil Ghani 17.50 A 2-Categorical Presentation of Term Graph Rewriting by Andrea Corradini, Fabio Gadducci FRIDAY, 5 September 09.00 Invited Talk: Barry Jay 10.15 Coffee Break 10.40 Presheaf Models for the pi-Calculus by Gian Luca Cattani, Ian Stark, Glynn Winskel 11.20 Categorical Modelling of Structural Operational Rules: case studies by Daniele Turi 12.00 Specifying Interaction Categories by Dusko Pavlovic, Samson Abramsky 12.40 Lunch 14.45 Invited Talk: Gordon Plotkin 16.00 Coffee Break 16.30 Lifting by A. Bucalo, G. Rosolini 17.10 General Synthetic Domain Theory -- A Logical Approach by Bernhard Reus, Thomas Streicher 17.50 Discussion on CTCS 20.00 Conference Dinner SATURDAY, 6 September 09.00 Shedding New Light in the World of Logical Systems by Uwe Wolter, Alfio Martini 09.40 Combining and Representing Logical Systems by Till Mossakowski, Andrzej Tarlecki, Wieslaw Pawlowski 10.20 Coffee Break 10.50 A decision algorithm for linear isomorphism of types O(nlog^2n) by Alexander Andreev, Sergei Soloviev 11.30 Effectiveness of the Global Modulus of Continuity on Metric Spaces by Klaus Weihrauch, Xizhong Zheng 12.30 Lunch Free Afternoon -----------------------------------------------------------------------------

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Preprint available
by Dr. P.T. Johnstone 30 Jul '97

30 Jul '97

The Pure Mathematics Department of Cambridge University has a new electronic preprint server (accessible via our home page at http://www.pmms.cam.ac.uk) The first preprint available may be of interest to people on the categories mailing list: it is C. Butz and P.T. Johnstone: Classifying toposes for first-order theories Abstract: By a classifying topos for a first-order theory $\Bbb T$, we mean a topos $\cal E$ such that, for any topos $\cal F$, models of $\Bbb T$ in $\cal F$ correspond exactly to open geometric morphisms ${\cal F} \rightarrow{\cal E}$. We show that not every (infinitary) first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate `smallness condition', and we show that every Grothendieck topos arises as the classifying topos of such a theory. We also show that every first-order theory has a conservative extension to one which possesses a classifying topos, and we obtain a Heyting-valued completeness theorem for infinitary first-order logic. For those who would prefer to receive a hard copy of this paper, I shall be bringing a supply with me to the Vancouver meeting. Peter Johnstone

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final CFP - Computing: The 4th Australiasian Theory Symposium (CATS98)
by lxue＠cs.uwa.edu.au 29 Jul '97

29 Jul '97

CALL FOR PAPERS CATS'98 - Computing: The Australasian Theory Symposium University of Western Australia Perth, Western Australia 2-3 February, 1998 CATS'98 will be held at the University of Western Australia as part of the Australasian Computer Science Week (ACSW98) which also includes: . the Australasian Computer Science Conference (ACSC'98) . the Australasian Database Conference (ADC'98) . the Australasian Computer Architecture Conference (ACAC'98) Following on from CATS'94 in Sydney, CATS'96 in Melbourne, and CATS'97 in Sydney, CATS'98 aims at providing a forum for researchers in theoretical computer science. Typical, but not exclusive, topics of interest include: - Algorithms and data structure - Category theory - Complexity - Computational algebra, biology, geometry, logic, and number theory - Concurrency - Distributed and parallel computing - Formal semantics, specification, synthesis, and verification Original research papers are solicited. Submissions to CATS'98 this year will be again conducted electronically, and should be sent in standard Postscript format to cats98(a)cs.uwa.edu.au by the submission deadline. Authors unable to access e-mail may send 4 hard copies of their papers to the program committee chair: Xuemin Lin -- CATS'98 Department of Computer Science University of Western Australia Crawley, Western Australia 6907 Australia E-mail: cats98(a)cs.uwa.edu.au http://www.cs.uwa.edu.au:80/~lxue/CATS98/index.html In both cases, confirmation of receipt will be given, in the case of a postscript submission, once the file has been successfully printed. Submissions should include an abstract, 3-6 key words, and the fax number and e-mail address of the corresponding author. The contribution of the paper should be clearly explained in both general and technical terms, and authors should make every effort to ensure the technical content of their papers is understandable by a broad audience. The paper (an extended abstract or full paper) should not exceed 15 A4 pages using 11 point or larger font. Submission of a paper should be regarded as an undertaking that, should the paper be accepted, at least one of the authors will attend the conference to present the work. Papers will be judged on originality, significance, correctness, and clarity. Accepted papers will be published in the proceedings of the Symposium, which will appear in the DMTCS series of Springer-Verlag. ========================================= INVITED SPEAKERS: Ming Li (University of Waterloo, Canada) Takeshi Tokuyama (IBM, Japan) ========================================= IMPORTANT DATES: Submission Deadline: Friday 15 August 1997. This is a hard deadline; submissions postmarked after this date will be returned. Author Notification: Friday 24 October 1997. Final Version: Friday 14 November 1997. Acceptance of papers for the conference will be conditional upon the registration of at least one of the authors by 21 November 1997. ========================================= GENERAL CHAIR: James Harland RMIT PROGRAM COMMITTEE CHAIR: Xuemin Lin UWA LOCAL CHAIR: Chi-Ping Tsang UWA STEERING COMMITTEE: John Crossley Monash University Peter Eades University of Newcastle James Harland RMIT Michael Johnson Macquarie University John Staples University of Queensland Harald Sondergaard University of Melbourne PROGRAM COMMITTEE: Cristian Calude University of Auckland Hossam Elgindy University of Newcastle Matthew Hennessy University of Sussex Xuemin Lin University of Western Australia Bruce Maggs Carnegie-Mellon University Martin Odersky University of South Australia Hong Shen Griffith University Harald Sondergaard University of Melbourne Antonios Symvonis University of Sydney Tadao Takaoka University of Canterbury Ron van der Meyden University of Technology, Sydney Lusheng Wang City University of Hong Kong Sue Whitesides McGill University David Wolfram Australian National University ===================================== ADDRESS FOR ALL PAPER SUBMISSION CORRESPONDENCE Xuemin Lin -- CATS'98 Department of Computer Science University of Western Australia Crawley, Western Australia 6907 Australia Telephone: +61 9 380 3449 Facsimile: +61 9 380 1089 E-mail: cats98(a)cs.uwa.edu.au ===================================== ADDRESS FOR CORRESPONDENCE, OTHER THAN PAPER SUBMISSION, RELATED TO ANY CONFERENCE FORMING PART OF THE AUSTRALIAN COMPUTER SCIENCE WEEK ACSW'98 Information Department of Computer Science The University of Western Australia Crawley, Western Australia, 6907 Telephone: +61 9 380 2533 Email: acsw98info(a)cs.uwa.edu.au ORGANISING COMMITTEE CHAIR Chris McDonald Department of Computer Science The University of Western Australia Crawley, Western Australia, 6907 Email: chris(a)cs.uwa.edu.au ACSW'98 Hosts: Department of Computer Science, The University of Western Australia Department of Computer Science, Curtin University of Technology Department of Computer Science, Edith Cowan University Computer Science Programme, Murdoch University

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functions Omega->Omega
by Paul Taylor 14 Jul '97

14 Jul '97

Richard Wood mentioned an observation about functions Omega->Omega in a topos. In the more abstract situation of a classifier Sigma for some subclass of monos (closed under isomorphisms, composition and pullback along arbitrary maps, and such that the characteristic function of a subobject, where it exists, is unique), the following formula holds: for any function f:Sigma x X -> X and predicate a:X -> Sigma f(a) & a = f(true) & a In fact, along with Sigma being a semilattice, this is necessary and sufficient for Sigma and its powers to form a full subcategory of some category in which Sigma is a classifier. I wonder whether anyone has noticed this formula before? In my construction, the Frobenius law for an existential quantifier is derivable from it. It is also reminiscent of the Berry order in stable domain theory, but I can see no substantial connection. It is easily provable in higher order logic: either way, assume a, so a=true. Curiously, Phoa's Principle (in synthetic domain theory) is the conjunction of the higher order equation above its lattice dual f(a) \/ a = f(false) \/ a and all functions f:Sigma->Sigma are monotone. For the continuation of this story, go to Vancouver ... Paul

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Interesting item for categories
by Michael Barr 11 Jul '97

11 Jul '97

I just got this from Adam. I think it might be interesting to post. Mike >>From adamba(a)microsoft.com Fri Jul 11 14:09:13 1997 Received: from mail5.microsoft.com (mail5.microsoft.com [131.107.3.31]) by triples.math.mcgill.ca (8.6.8/8.6.6) with ESMTP id OAA04707 for <barr(a)triples.math.mcgill.ca>; Fri, 11 Jul 1997 14:09:12 -0400 Received: by mail5.microsoft.com with Internet Mail Service (5.0.1458.49) id <3W9L4D7D>; Fri, 11 Jul 1997 11:16:22 -0700 Message-ID: <9D311811F5DFD011A37800805FD4BA8803A91B(a)RED-66-MSG.dns.microsoft.com> From: "Adam Barr (Win NT)" <adamba(a)microsoft.com> To: "'barr(a)triples.math.mcgill.ca'" <barr(a)triples.math.mcgill.ca> Subject: lecture abstract Date: Fri, 11 Jul 1997 11:14:29 -0700 X-Priority: 3 X-Mailer: Internet Mail Service (5.0.1458.49) Status: R This is a talk at Microsoft -- the abstract mentions category theory!! - adam ************************************************************************ ******** WHO: Erik Meijer AFFILIATION: Utrecht University, The Netherlands TITLE: The Next 700 Scripting Languages, or COM meets Functional Programming WHEN: Wednesday July 16, 1997 WHERE: 9s/1007 TIME: 3:00-4:30 HOST: Conal Elliott VIDEO Not Available ************************************************************************ ******* Please pass on this information to any other interested internal employees. The Next 700 Scripting Languages, or COM meets Functional Programming More than 30 years ago, Peter Landin proposed to define domain specific languages by embedding them into the purely functional host language ISWIM. The host language captures how things are described in terms of other things, and is specialized for a certain problem domain by an appropriate choice of primitive operations. In 1997-speak, we would say that Landin proposed to have a single scripting language to glue together application specific software components. This is very similar to using Visual Basic for scripting COM/ActiveX components. For a purely functional language however, it is easier said than done; especially if we want to introduce impure, side-effecting, primitives. Surprisingly, it turns out that the concept of monads from category theory provides an elegant solution to the problem of integrating interaction in a purely functional language. Finally, after 30 years, Landin's idea can be put into practice, and Fran, Haskell/CGI, Haskore, Tk/Gofer, AgentScript, and the Haskell-COM integration are collectively becoming a nice proof of concept. In this talk we will argue why we think lazy functional language (such as Haskell) are especially suited as scripting languages as they allow users to define their own control structures, or as we say, combinators. During the talk, the Microsoft Agent genie will navigate the Microsoft internet Explorer through a tour of dynamically generated HTML pages, everything scripted in Haskell. Biography ======= Erik Meijer is currently a visiting research professor at the Oregon Graduate Institute, on leave from Utrecht University in The Netherlands. He is known from his theoretical work on functional programming (Squiggol) and compiler construction, but now spends his time on practical applications of functional programming, especially promoting them as scripting languages. He is recently working on making COM components available from Haskell and encapsulating Haskell programs as COM components, and is a member of the Standard Haskell Committee. Home Page : http://tibet.cse.ogi.edu/Personal/Default.html" . msrlecture

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Tuesday evening at CT97, future of publication
by Art Stone 11 Jul '97

11 Jul '97

The Tuesday evening of CT97, 15 July, we contemplate having an open discussion on the future of publication in category theory. Questions that are likely to come up: Are the paper publications really dying? (With diminishing library budgets, one Vancouver area university has been forced to cancel both Cahiers and JPAA, and with limited library space, no longer has available on its shelves journals more than 10 or 15 years old.) How do we provide for archiving in such a situation? What are the opinions of the current editors of our journals? We're fortunate to have TAC. Is there need for a wider range of styles of publication? What are the alternatives? Is CD-ROM a possibility? (Might it give us again the freedom we had in the early volumes of Springer's LNM -- or would that be a good thing?) Would it be better to have an e-archive, like q-alg? How? Where? Would it be secure, a lasting archive? What is to be learned from existing or past examples: Imperial College, Hypatia, triples.math.mcgill, the Sydney category seminar? Frequently papers appear which the authors subsequently wish they could change. And terminology changes over time -- as we begin to understand what it was we were trying to say. Might we want to have "papers" or "books" that can be modified over time (with ongoing version numbers as we have now for software)? For the most basic and important works, might we prefer something that approaches what Bourbaki intended to give us: works that would evolve over time and never to go out of date? (Bourbaki's vision preceded the development of media that would make it possible.) And how do we want to treat the proceedings of CT97? At first, papers should be available by ftp on math.ubc.ca, but what do we want in the long run? Art Stone

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European School on Graph Transformation
by Frank Drewes 11 Jul '97

11 Jul '97

************************************************* * First Call for Participation * * European School on Graph Transformation * * * * Bremen (Germany) * * March 2-7, 1998 * ************************************************* [for a PostScript version of this call see http://www.informatik.uni-bremen.de/grp/ag-ti/getgrats] Aims and Scope Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas it includes software specification and development, VLSI layout schemes, massively parallel computer architectures, database design, modeling of concurrent systems, logic programming, computer animation, developmental biology, music composition, visual languages, and many others. The area of graph grammars and graph transformation generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact within the area of graph grammars, graph transformation is considered a fundamental programming paradigm where computation includes specification, programming, and implementation. The main goal of the School is to disseminate ``the basic knowledge'' about the area of graph grammars and graph transformation and to present in a systematic way the state of the art and the recent advances in the theory and applications of graph transformation systems. The aim is to bring together students, young researchers and senior scientists interested in the area. The expected audience for the School consists of two groups: (i) participants from outside the area: these are the students and researchers who want to learn (for various reasons) about graph grammars and graph transformation, (ii) participants from inside the area: these are students and researchers that already have some knowledge of graph grammars, but they are interested to get a more systematic insight into the area. The objective of the School (especially as the first group is concerned) is to make the participants ``literate'' in the area of graph grammars and graph transformation. This means that, after the School, the participants will find it easier to follow basic literature, and to consider applications of graph grammars and graph transformations in their areas of interest. The program of the School covers main developments in both theory and applications of graph transformation. Certificates The School will issue certificates to acknowledge a successful participation. Organization The School is one of the main events organized by the TMR Research Network GETGRATS (General Theory of Graph Transformation Systems). Also, the ESPRIT Working Group APPLIGRAPH (Applications of Graph Transformation) participates in the organization of the school. Program Committee Michel Bauderon, Hartmut Ehrig, Dirk Janssens, Hans-Joerg Kreowski (Cochair), Ugo Montanari, Francesco Parisi-Presicce, Grzegorz Rozenberg (Chair) Organizing Committee Frank Drewes, Hans-Joerg Kreowski (Chair), Grzegorz Rozenberg Grants The organizers hope to be able to offer grants to cover (parts of) the costs for travel and subsistence. Information For more information please contact the organizers by email ({drewes,kreo}(a)informatik.uni-bremen.de) You can also look up the WWW homepage of the School. Just follow the respective link at http://www.informatik.uni-bremen.de/grp/ag-ti/getgrats. Registration To register for the School please return the form at the end before December 6, 1997. Pre-registrations (without obligation) are welcome at any time. The registration fee will be around DM 1200,- - DM 1300,-. This covers lodging (6-7 nights), full board, and the teaching material including the handbook. Scientific Programme The scientific programme consists of 4 parts: INTRODUCTORY LECTURE provides an informal panoramic sketch of the area. BASIC CORE covers basic approaches to defining graph transformations. Each of the following four approaches is covered by a strand of lectures. (1) node rewriting (2) (hyper)edge rewriting (3) logical descriptions (4) algebraic approaches LAYER 1 consists of lectures on various ways of defining graph transformations not covered in the Basic Core, as well as various specialistic topics from the 4 strands of the Basic Core. (1) term graph rewriting (2) foundations of the PROGRES approach (3) concurrency (4) coordination (5) 2-structures (6) pullback-approach (7) high-level approaches LAYER 2 consists of lectures covering various applications of graph transformation and topics strongly rooted in applications. (1) term graph rewriting in functional programming (2) the use of PROGRES in a software engineering environment (3) modularization (4) distributed algorithms (5) visual design of distributed systems (6) image generation (7) graph drawing The lectures will be given by leading experts in the field of graph grammars and graph transformation. Presentation of Tools In addition to the scientific programme various systems and tools (PROGRES, AGG, GRAPHED, CLEAN, COLLAGE-VR, etc.) will be presented. Teaching Material - copies of transparencies, relevant papers, and lecture notes - the Handbook on Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations, World Scientific 1997 -------------------------- Registration form --------------------------- I would like to [ ] pre-register / [ ] register for the European School on Graph Transformation. Name: ____________________________________ Position: ____________________________________ Address: ____________________________________ ____________________________________ ____________________________________ ____________________________________ email and fax: ____________________________________ I need financial support: [ ] yes [ ] no (Please return this form to Prof. Dr. Hans-Joerg Kreowski, Universitaet Bremen Fachbereich 3 Postfach 330440 D-28334 Bremen (Germany) email: kreo(a)informatik.uni-bremen.de Fax: +49-421-218-4322)

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Re: What is q-alg ????????????????????
by James Stasheff 11 Jul '97

11 Jul '97

Some of you have asked: what is q-alg? q-alg(a)eprints.math.duke.edu is a fully automated electronic archive and distribution server for papers on QUANTUM ALGEBRA AND TOPOLOGY (INCLUDING KNOT THEORY) (starting from Dec, 1994) This is an eprint archive for mathematics papers on ``quantum algebraic'' topics such as quantum groups (also known as noncommutative Hopf algebras) and related constructions, representations of affine Lie algebras, vertex operator algebras and operads, algebraic aspects of the KP and Toda lattice hierarchies, etc. (JDS: although not listed explicitly, category theroy, especially higher dim cats, is certainly appropriately posted to this server) For the time being, the archive also welcomes submissions of mathematics papers on modern knot theory (Jones and HOMFLY polynomials, Reshetikin-Turaev invariants, etc.). A separate archive will be formed for knot theory when the traffic becomes sufficient to warrant it. Papers submitted to this archive should be intended for an audience of mathematicians; we also welcome cross-listings of appropriate papers from physics or other fields which are archived elsewhere. Other mathematics archives running the same software: o alg-geom(a)eprints.math.duke.edu Algebraic Geometry o auto-fms(a)msri.org Automorphic Forms o cd-hg(a)msri.org Complex Dynamics and Hyperbolic Geometry o dg-ga(a)msri.org Differential Geometry and Global Analysis o q-alg(a)eprints.math.duke.edu Quantum Algebra (including Knot Theory) For information about archives in other fields, consult http://xxx.lanl.gov/help/ ------------------------------------------------------------------------- ------------------------------------------------------------------------- In the generic xxx help text, substitute q-alg(a)eprints.math.duke.edu for the generic e-mail address arch-ive(a)xxx.lanl.gov ------------------------------------------------------------------------- ------------------------------------------------------------------------- Outgoing mail from the e-print archive has the username no-reply (to avoid problems due to occasional mail that bounces back). Commands to the system should always be sent to arch-ive(a)xxx.lanl.gov with the command in the subject field (e.g. Subject: help). Only one command at a time is accepted. Subscribers automatically receive a listing of new titles/abstracts on days papers are received. You will have a more pleasurable time using the archives if you read this file carefully, read ALL responses you get to your interactions with the archives, and follow the instructions therein. This help file summarizes the email interface commands. This information can be more easily accessed via the WorldWideWeb at http://xxx.lanl.gov/help/ . ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds(a)math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds(a)math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250

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un peu de r'eclame
by Pierre Ageron 09 Jul '97

09 Jul '97

Let me advertise for some more or less recent work of mine about sketches/accessible categories (not available electronically, but I'll be happy to send reprints or preprints on request). ------- (1) Cat'egories accessibles `a limites projectives non vides et cat'egories accessibles `a limites projectives finies Diagrammes 34 (1995) 1-10 For fixed b, b-accessible categories with non-empty limits are characterized as the categories of models of specific sketches. As a corollary, the category of these categories is Cartesian closed. (Proved independantly by Ad'amek.) Accessible categories with finite limits are also characterized. ------- (2) Effective taxonomies and crossed taxonomies Cahiers de Top. et de G'eom. Diff. Cat. XXXVII (1996) 82-90 A taxonomy is a "category without identities". This bare structure is somewhat dull, but "crossed modules of taxonomies" seem more interesting. In the latter structure, "Dedekind-finite" objects play a role similar to that of finitely presentable objects in a category. A notion similar to that of accessibility can thus be defined. ------- (3) La tour holomorphe d'une esquisse Cahiers de Top. et de G'eom. Diff. Cat. XXXVII (1996) 295-314 A construction of Lair's in the category of sketches is revisited and noticed to specialize to the construction of the holomorph when restricted to groups. The iteration of this construction reveals two invariants of a sketch: an ordinal and a group. Some explicit computations are provided. ------- (4) Cat'egories accessibles `a produits fibr'es (preprint) Continuation of (1). Accessible categories with (finite) pullbacks are characterized in terms of sketches. This is achieved by introducing "free" colimits in Set: such colimits are proved to be exactly those that commute with pullbacks. ------- (5) Limites projectives conditionnelles dans les cat'egories accessibles (preprint) For fixed b, those b-accessible categories s.t. every diagram with a cone has a limit are characterized in terms of sketches. As a corollary, the category of these categories is Cartesian closed. Similarly for those b-accessible categories s.t. every non-empty diagram with a cone has a limit, or for those with "consistent wide pullbacks". ------- PIERRE AGERON 1) coordonnees bureau adresse : mathematiques, Universite de Caen, 14032 Caen Cedex telephone : 02 31 56 57 37 telecopie : 02 31 93 02 53 adresse electronique : ageron(a)math.unicaen.fr 2) coordonnees domicile adresse : 28 rue de Formigny 14000 Caen telephone : 02 31 84 39 67

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