February 2003 - Categories - categories.org.au

More Topos questions ala "Conceptual Mathematics"
by Galchin Vasili 11 Jun '03

11 Jun '03

Hello, 1) In the very last chapter (Session 33 "2: Toposes and logic" of "Conceptual Mathematics" where the authors cover topoi, they define '=>' for the internal Heyting algebra of Omega: "Another logical operation is 'implication', which is denoted '=>'. This is also a map Omega x Omega->Omega, defined as the classifying map of the subobject S 'hook' Omega x Omega determined by the all those <alpha, beta> in Omega x Omega such that alpha "subset of" beta." Starting from "subobject S 'hook" ......" I got totally lost. I am frustrated because I know this is crucial to understanding why Omega is an internal Heyting algebra, so any help would be appreciated. (I am assuming that alpha and beta are subojects of Omega???). 2) In the same Session 33 on pg 350 is a set "rules of logic". These are exactly the axioms for a Heyting algebra, yes? Regards, Bill Halchin

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projective algebras
by Andrei Popescu 04 Mar '03

04 Mar '03

Dear Categorists, Some time ago, I have posed you a question about the characterization of projective algebras in the category of all algebras of a given signature. Since some of you appeard interested in the subject, I allow myself to send you, in a slightly detailed manner, the answer that I have found. Projective algebras coincide with free algebras in the following cases: I. Any class (i.e. complete subcategory) of algebras that is closed to taking subobjects and for which free algebras exist and have a certain property (namely that there are no infinite chains of elements such that each one is obtained by applying an operation to an n-uple that includes the predecesor in the chain). In particular, II. Suppose X is a countably infinite set. Any quasivariety K of algebras for which the kernel of the unique morphism extending X from the term algebra to the algebra freely generated in K by X has finite congruence classes. In particular, III. - The category of all algebras (of a given signature); - The category of [commutative] semigroups; - The category of [commutative] (non-unital and non-anihilating) semirings. Best regards, Andrei

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Preprint: Adjoints for double categories
by grandis＠dima.unige.it 28 Feb '03

28 Feb '03

The following preprint is available, in ps: M. Grandis - R. Pare´ Adjoints for double categories Dip. Mat. Univ. Genova, Preprint 476 (2003), 40 p. http://www.dima.unige.it/~grandis/Dbl.Adj.ps Abstract. After 'Limits in double categories' (Cahiers Topologie Geom. Differentielle Categ. 40 (1999), 162-220), we pursue our study of the general theory of weak double categories, addressing adjunctions and monads. A general 'double adjunction', which appears often in concrete constructions, has a *colax* double functor left adjoint to a *lax* one. This cannot be viewed as an adjunction in some bicategory, because lax and colax morphisms do not compose well and do not form one. However, such adjunctions live within an interesting construct, the strict double category of weak double categories, with horizontal and vertical arrows provided by the lax and colax double functors, respectively, and a suitable notion of double cell. Marco Grandis Dipartimento di Matematica Universita` di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis(a)dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/

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Lectureship positions
by A.Kurz 28 Feb '03

28 Feb '03

At the department of Mathematics and Computer Science of the University of Leicester are two lectureship postions available. They are advertised for the area of Software Engeneering but, to cite from the official announcement at http://www.le.ac.uk/personnel/jobs/a5549.html, "outstanding applicants with expertise in any related area of Computer Science are welcomed". Deadline is March 21. Many Greetings, Alexander -- http://www.mcs.le.ac.uk/~akurz

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Topos: IL theorem prover
by Galchin Vasili 27 Feb '03

27 Feb '03

Hello, Here is an intuitionistic logic theorem prover that might be interesting in light of the relationship of Heyting algebras to topoi: http://www.intellektik.informatik.tu-darmstadt.de/~jeotten/ileanTAP/ Regards, Bill Halchin

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CFP: INT'L CONF ON ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS
by japaridze g 27 Feb '03

27 Feb '03

<We apologize for multiple postings.> INTERNATIONAL CONFERENCE ON ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS Tbilisi, Georgia, 7 - 11 July 2003 The aim of this conference is to present some recent advances in the use of algebraic, order-theoretic, and topological methods in non-classical logics. We also hope to bring together researchers in the fields of non-classical logics, lattice theory, universal algebra, category theory, and general topology in order to foster collaboration and to get new ideas for further research. CONFERENCE TOPICS: Lattices with operators Topological semantics of modal logic Topological and topos semantics of intuitionistic logic Ordered topological spaces. INVITED SPEAKERS: Johan van Benthem, University of Amsterdam Leo Esakia, Georgian Academy of Sciences Mai Gehrke, New Mexico State University John Harding, New Mexico State University Ramon Jansana, University of Barcelona Joachim Lambek, McGill University Daniele Mundici, Milan University Yde Venema, University of Amsterdam Michael Zakharyaschev, King's College Marek Zawadowski, University of Warsaw CALL FOR PAPERS: If you wish to speak at the conference, please send by email a title and abstract of your talk to Guram Bezhanishvili (gbezhani(a)nmsu.edu) The deadline for submissions is 1 May. We will let you know by 15 May if you will be invited to speak at the conference. The deadline to register for the conference is 1 June. LOCATION: Tbilisi State University, Tbilisi, Georgia WEB SITE: http://piscopia.nmsu.edu/morandi/TbilisiConference IMPORTANT DATES: Submission deadline: 1 May 2003 Notification of acceptance: 15 May 2003 Registration deadline: 1 June 2003 Conference: 7 - 11 July 2003 PROGRAM COMMITTEE: Guram Bezhanishvili, New Mexico State University Patrick Morandi, New Mexico State University Willem Blok, University of Illinois at Chicago Roberto Cignoli, University of Buenos Aires Josep Maria Font, University of Barcelona Dick de Jongh, University of Amsterdam Larisa Maksimova, Russian Academy of Sciences, Novosibirsk Hiroakira Ono, Japan Advanced Institute of Science and Technology Rohit Parikh, City University of New York Lazare Zambakhidze, Tbilisi State University ORGANIZATIONAL COMMITTEE: Merab Abashidze, Georgian Academy of Sciences Nick Arevadze, Georgian Academy of Sciences Nick Bezhanishvili, University of Amsterdam David Gabelaia, King's College Revaz Grigolia, Georgian Academy of Sciences Giorgi Japaridze, Villanova University Mamuka Jibladze, Georgian Academy of Sciences Ioseb Khutsishvili, Tbilisi State University Dimitri Pataraia, Georgian Academy of Sciences Levan Uridia, Tbilisi State University ORGANIZING INSTITUTIONS: New Mexico State University Tbilisi State University Georgian Academy of Sciences This conference is part of the activity of a grant funded by the Civil Research Development Fund and the Georgian Research Development Fund. For further information, contact Guram Bezhanishvili (gbezhani(a)nmsu.edu) or Pat Morandi (pmorandi(a)nmsu.edu)

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Lamarche casuistries paper
by Vaughan Pratt 26 Feb '03

26 Feb '03

I seem to have misplaced my copy of Francois Lamarche's paper on casuistries. I'd be very grateful for either an online copy or Francois' current email address (preferably both). Vaughan Pratt

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Workshop on categorical methods for concurrency....
by A.Kurz 25 Feb '03

25 Feb '03

3 Debian/1.0.0-0.woody.1 X-Accept-Language: en MIME-Version: 1.0 To: categories(a)mta.ca Subject: categories: CfP: CMCIM'03 Content-Type: text/plain; charset=3DISO-8859-1; format=3Dflowed Content-Transfer-Encoding: 8bit Sender: cat-dist(a)mta.ca Precedence: bulk [ Apologies for multiple copies ] Workshop on CATEGORICAL METHODS FOR CONCURRENCY, INTERACTION, AND MOBILITY Marseille, France, 6 September 2003 affiliated with CONCUR 2003 and held together with GETCO 2003 Call for Papers See also: http://www.mcs.le.ac.uk/events/cmcim03 Aims and Scope: The aim of the workshop is to bring together researchers applying category theory to concurrency, interaction, or mobility. Topics of interest include, but are not limited to: categorical algebras of processes categorical methods in game semantics and geometry of interaction categorical models of term/graph rewriting or rewriting logic Chu spaces coalgebras, bialgebras, coinduction comparing models of concurrency enriched categories of processes interaction categories presheaf models GETCO'03: Due to the close relation between geometric and topological methods on the one hand and categorical methods on the other hand, CMCIM'03 will be held jointly with the workshop on Geometric and Toplogical Methods in Concurrency Theory (GETCO'03). Both workshops will be on the same day with their talks not overlapping. Invited Lecture: Glynn Winskel Programme Committee: Marcelo Fiore (Cambridge) Eric Goubault (Paris) Thomas Hildebrandt (Copenhagen) Alexander Kurz (Leicester) Ugo Montanari (Pisa) John Power (Edinburgh) Jan Rutten (Amsterdam) Peter Selinger (Ottawa) Glynn Winskel (Cambridge) Important dates: Deadline for submission: June 1 Notification of acceptance: July 7 Final version due: July 27 Workshop dates: September 6 Location: The workshop will be held in Marseille. It is a satellite workshop of CONCUR 2003. For venue and registration see the CONCUR web page at http://concur03.univ-mrs.fr Submissions: It is planned to publish the proceedings of the meeting as a volume in Elsevier's ENTCS series. Papers must contain original contributions. Papers should be submitted as PostScript files by email to cmcim03(a)mcs.le.ac.uk, containing `CMCIM-submission' in the subject. A separate message should also be sent (subject: CMCIM-abstract), containing authors, title, and a text-only abstract. Workshop organizers: Thomas Hildebrandt BRICS, DAIMI, Computer Science Deptartment, University of Aarhus, Ny Munkegade, B. 540, 8000 =C5rhus C, DK Alexander Kurz Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH. Email: cmcim03(a)mcs.le.ac.uk Further information at http://www.mcs.le.ac.uk/events/cmcim03

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LICS 2003 Call for Short Presentations
by Alex Simpson 24 Feb '03

24 Feb '03

**************** Submission Deadline is MARCH 21, 2003 ********************* Eighteenth Annual IEEE Symposium on LOGIC IN COMPUTER SCIENCE June 22nd - 25th, 2003, Ottawa, Canada http://www.lfcs.informatics.ed.ac.uk/lics CALL FOR SHORT PRESENTATIONS The LICS Symposium is an annual international forum on theoretical and practical topics in computer science that relate to logic in a broad sense. LICS 2003 will take place in Ottawa, Canada, June 22-25, 2003 and will feature invited talks, invited tutorials, and presentations of papers that will appear in the LICS 2003 proceedings. In addition, LICS 2003 will have a session of short (5-10 minutes) presentations. This session is intended for descriptions of work in progress, student projects, and relevant research being published elsewhere; other brief communications may be acceptable. Submissions for these presentations, in the form of short abstracts (1 or 2 pages long), should be entered by following the "Instructions for short presentations" link at the LICS 2003 website http://www.lfcs.informatics.ed.ac.uk/lics/lics03 between March 17th and March 21st, 2003. Authors will be notified of acceptance or rejection by April 4th, 2003. Suggested, but not exclusive, topics of interest for submissions include: automata theory, automated deduction, categorical models and logics, concurrency and distributed computation, constraint programming, constructive mathematics, database theory, domain theory, finite model theory, formal aspects of program analysis, formal methods, hybrid systems, lambda and combinatory calculi, linear logic, logical aspects of computational complexity, logics in artificial intelligence, logics of programs, logic programming, modal and temporal logics, model checking, programming language semantics, reasoning about security, rewriting, specifications, type systems and type theory, and verification. Program Chair: Phokion G. Kolaitis Computer Science Department University of California, Santa Cruz Santa Cruz, CA 95064, USA Email: kolaitis(a)cs.ucsc.edu Phone: + 1 831 459 4768 Fax: + 1 831 459 4829 Program Committee: Michael Benedikt, Bell Laboratories Andreas R. Blass, University of Michigan Maria Luisa Bonet, UPC, Barcelona Witold Charatonik, University of Wroclaw Marcelo Fiore, University of Cambridge Giorgio Ghelli, Universita di Pisa Thomas A. Henzinger, UC Berkeley Alan Jeffrey, DePaul University Assaf J. Kfoury, Boston University Phokion G. Kolaitis, UC Santa Cruz Orna Kupferman, Hebrew University of Jerusalem Ursula Martin, University of St Andrews Paul-Andre Mellies, CNRS & University of Paris 7 Eugenio Moggi, Universita di Genova Ugo Montanari, Universita di Pisa Paliath Narendran, University at Albany SUNY Luke Ong, University of Oxford & National University of Singapore Martin Otto, University of Wales Swansea Frank Pfenning, Carnegie Mellon University Mirek Truszczynski, University of Kentucky

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Category of directed multigraphs with loops
by Galchin Vasili 24 Feb '03

24 Feb '03

Hello, Given two graphs, A and B, I am trying figure out how to construct the product AxB. I have been rereading "Conceptual Mathemtatics" by Lawvere. The category of irreflexive graphs is one of the running examples throughout the book. I have been concentrating on the chapters concerned with the product of objects, but I don't see any details of how to construct AxB. Have I skipped over something? Regards, Bill Halchin

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