September 2006 - Categories - categories.org.au

Foundations?
by F W Lawvere 03 Sep '10

03 Sep '10

Down with "Foundations"! Up with algebra! Dear Friends, Presumably I am among those who are being "vilified" as "lovers of categories as foundation". By avoiding any precise definition, such a formulation might appeal to the widespread justified boredom induced by the past hundred years of "foundations as justification". Whenever I used the word "foundation" in my writings over the past forty years, I have explicitly rejected that reactionary use of the term and instead used the definition implicit in the work of my teachers Truesdell and Eilenberg. Namely, an important component of mathematical practice is the careful study of historical and contemporary analysis, geometry, etc. to extract the essential recurring concepts and constructions; making those concepts and constructions (such as homomorphism, functional, adjoint functor, etc.) explicit provides powerful guidance for further unified development of all mathematical subjects, old and new. What is the primary tool for such summing up of the essence of ongoing mathematics? Algebra! Nodal points in the progress of this kind of research occur when, as is the case with the finite number of axioms for the metacategory of categories, all that we know so far can be expressed in a single sort of algebra. I am proud to have participated with Eilenberg, Mac Lane, Freyd, and many others, in bringing about the contemporary awareness of Algebra as Category Theory Had it not been for the century of excessive attention given to the alleged possibility that mathematics is inconsistent, with the accompanying degradation of the F-word, we would still be using it in the sense known to the general public: the search for what is "basic". We, who supposedly know the explicit algebra of homomorphisms, functionals, etc. are long remiss in our duty to find ways to utilize those concepts also in guiding high school calculus. Best wishes, Bill Bibliography: - The Category of Categories as a Foundation for Mathematics, La Jolla conference 1965, Springer (1966) - Adjointness in Foundations, Dialectica, (1969), to be reprinted in TAC - Foundations and Applications: Axiomatization and Education, Bulletin of Symbolic Logic, (2003) vol 9, pp 213-224 - Sets for Mathematics, w/ Bob Rosebrugh, Cambridge Univ. Press, (2003) ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************

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papers available
by tholen＠mathstat.yorku.ca 30 Sep '06

30 Sep '06

I have made the following recent papers available from my home page at www.math.yorku.ca/~tholen I appreciate receiving any comments that you may have. Regards, Walter. ------------------------------------- Marco Grandis and Walter Tholen: Natural weak factorization systems Abstract. In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category K is introduced, as a pair (comonad, monad) over K^2. The link with existing notions in terms of morphism classes is given via the respective Eilenberg-Moore categories. ------------------------------------- Jiri Rosicky and Walter Tholen: Factorization, fibration and torsion Abstract. A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3-for-2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and of weak factorization system, as used in abstract homotopy theory. ------------------------------------- Eraldo Giuli and Walter Tholen: A topologist's view of Chu spaces Abstract. For a symmetric monoidal-closed category X and any object K, the category of K-Chu spaces is small-topological over X and small-cotopological over X^op. It's full subcategory of M-extensive K-Chu spaces is topological over X when X is M-complete, for any morphism class M. Often they form a full coreflective subcategory of Diers' category of affine K-spaces. Hence, in addition to their roots in in the theory of pairs of topological vector spaces (Barr) and in the study of event structures for modeling concurrent processes (Pratt), Chu spaces seem to have a less explored link with algebraic geometry. We use the Zariski closure operator to characterize the self-dual category of M-extensive and M-coextensive K-Chu spaces.

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Workshop on Identity Types
by Erik Palmgren 27 Sep '06

27 Sep '06

Identity Types - Topological and Categorical Structure Workshop, November 13-14, 2006, Uppsala University. The identity type, the type of proof objects for the fundamental propositional equality, is one of the most intriguing constructions of intensional dependent type theory (also known as Martin-Löf type theory). Its complexity became apparent with the Hofmann-Streicher groupoid model of type theory. This model also hinted at some possible connections between type theory and homotopy theory and higher categories. Exploration of his connection is intended to be the main theme of this workshop. Preliminary list of speakers Steve Awodey (Pittsburgh) Peter Dybjer (Göteborg) Richard Garner (Uppsala) Martin Hyland (Cambridge, to be confirmed) Per Martin-Löf (Stockholm) Thomas Streicher (Darmstadt) Michael A Warren (Pittsburgh) A final list of speakers will be prepared shortly before the workshop. If you are interested in giving a talk, please submit a short abstract to the organiser before October 25. The working days of the meeting are November 13 and November 14 until noon. Organiser: Erik Palmgren, Uppsala University, email: palmgren(a)math.uu.se Venue: Uppsala University, Polacksbacken, Lägerhyddsvägen 1-2, Uppsala, Sweden. Accomodation is expected to be arranged by the participants themselves. See the workshop webpage for a list of recommended hotels and further information. Workshop webpage: www.math.uu.se/~palmgren/itt

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Are geometric categories balanced?
by Steve Vickers 26 Sep '06

26 Sep '06

Am I right in believing that geometric categories (Elephant A 1.4.18) need not be balanced? (I don't know a counterexample - the geometric categories that I can think of are all toposes.) The reason I ask is this. One is (or certainly I am) used to thinking of geometric logic as the logic of Grothendieck toposes. Grothendieck toposes are balanced, and consequently a sound reasoning principle in their internal logic is that functions are equivalent to total, single-valued relations. One therefore thinks of this as a principle of geometric reasoning. However, I suspect it doesn't follow just from the pure logic - the connectives and inference rules - of geometric logic. This would be verified if there are unbalanced geometric categories, since the pure logic is interpretable in arbitrary geometric categories. I would take this as indicating that we want geometric logic to be more than just what the pure logic says it is. The Elephant gives two different definitions of geometric theory: by the pure logic in D 1.1.6, and by a more general notion of geometric construct in B 4.2.7. It asserts their equivalence, but I think this must be with respect to a semantics already presumed to be in Grothendieck toposes. Steve Vickers.

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MFPS XXIII Call for Papers
by Michael Mislove 22 Sep '06

22 Sep '06

CALL FOR PAPERS MFPS XXIII <http://www.math.tulane.edu/~mfps/mfps23.htm> Twenty-third Conference on the Mathematical Foundations of Programming Semantics Tulane University New Orleans, LA USA April 11 - 14, 2007 Partially Supported by US Office of Naval Research The Twenty-third Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIII) will take place on the campus of Tulane University, New Orleans, LA USA from Wednesday, April 11 through Saturday, April 14, 2007. The MFPS conferences are devoted to those areas of mathematics, logic, and computer science which are related to models of computation, in general, and to the semantics of programming languages, in particular. The series has particularly stressed providing a forum where researchers in mathematics and computer science can meet and exchange ideas about problems of common interest. As the series also strives to maintain breadth in its scope, the conference strongly encourages participation by researchers in neighboring areas. The INVITED SPEAKERS for MFPS XXIII are Gerard Berry (Esterel Technologies) --- to be confirmed --- Stephen Brookes (CMU) Jane Hillston (Edinburgh) John Mitchell (Stanford) Gordon Plotkin (Edinburgh) John Power (Edinburgh) In addition, there will be three special sessions: 1. A special session honoring GORDON PLOTKIN on his 60th birthday year, organised by Samson Abramsky (Oxford). 2. A special session on SECURITY, organised by Catherine Meadows (NRL). 3. A special session on SYSTEMS BIOLOGY, organised by Jane Hillston (Edinburgh) and Prakash Panangaden (McGill). 4. A Special Session on Physics, Information and Computation organized by Keye Martin (NRL). Further, there will be a TUTORIAL DAY on April 11. The topic will be Domain Theory; the speakers will be announced at a later date. This event will be free to those who are interested in attending. The remainder of the program will consist of papers selected by the following PROGRAM COMMITTEE Samson Abramsky (Oxford) Michael Mislove (Tulane) Andrej Bauer (Ljubljana) John Mitchell (Stanford) Stephen Brookes (CMU) Eugenio Moggi (Genova) Pierre-Louis Curien (CNRS & Paris 7) Laurent Regnier (Marseille) Andrzej Filinski (Copenhagen) Giuseppe Rosolini (Genova) Marcelo Fiore (Cambridge), CHAIR Davide Sangiorgi (Bologna) Achim Jung (Birmingham) Philip Scott (Ottawa) Masahito Hasegawa (Kyoto) Daniele Varacca (Paris 7) Ursula Martin (QM London) James Worrell (Oxford) Catherine Meadows (NRL) Steve Zdancewic (Pennsylvania) from submissions received in response to this call for papers. TOPICS include, but are not limited to, the following: biocomputation; categorical models; concurrent and distributed computation; constructive mathematics; domain theory; formal languages; formal methods; game semantics; lambda calculus; logic; non-classical computation; probabilistic systems; process calculi; program analysis; programming- language theory; quantum computation; rewriting theory; security; specifications; topological models; type systems; type theory. The CONFERENCE PROCEEDINGS will be published by ENTCS (Electronic Notes in Theoretical Computer Science <http://www.entcs.org/>). Submission instructions, style files for preparing a submission, and a link to the MFPS XXIII submission site are available from the conference web page: http://www.math.tulane.edu/~mfps/mfps23.htm IMPORTANT DATES: * Fri Dec 15: Paper registration deadline, with short abstracts. * Fri Dec 22: Paper submission deadline. * Fri Feb 4: Author notification. * Fri Mar 2: Final versions for the proceedings. The Organising Committee for MFPS consists of Stephen Brookes (CMU), Achim Jung (Birmingham), Catherine Meadows (NRL), Michael Mislove (Tulane), and Prakash Panangaden (McGill). The local arrangements for MFPS XXIII are being overseen by Michael Mislove. =============================================== Professor Michael Mislove Phone: +1 504 862-3441 Department of Mathematics FAX: +1 504 865-5063 Tulane University URL: http://www.math.tulane.edu/~mwm New Orleans, LA 70118 USA ===============================================

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Octoberfest deadlines
by Richard Blute 21 Sep '06

21 Sep '06

Hi everyone, There are several deadlines fast approaching for people attending Octoberfest. Today, September 20th, is the last official day to get the reduced rate at the Quality Hotel, and Friday, September 22nd is the last day to submit an abstract for a talk. Abstracts should be submitted to Rick Blute at rblute(a)mathstat.uottawa.ca. (I will reply when I receive your abstract.) See our website for full details, including further accomodation info. http://aix1.uottawa.ca/~scpsg/Octoberfest06/Octoberfest06.prelim2.html See you all soon, Rick Blute Phil Scott

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WoLLIC'2007 - Call for Papers
by Ruy de Queiroz 18 Sep '06

18 Sep '06

[** sincere apologies for duplicates **] Call for Papers 14th Workshop on Logic, Language, Information and Computation (WoLLIC'2007) Rio de Janeiro, Brazil July 2-5, 2007 WoLLIC is an annual international forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning. Each meeting includes invited talks and tutorials as well as contributed papers. The Fourteenth WoLLIC will be held in Rio de Janeiro, Brazil, from July 2 to July 5, 2007, and sponsored by the Association for Symbolic Logic (ASL), the Interest Group in Pure and Applied Logics (IGPL), the European Association for Logic, Language and Information (FoLLI), the European Association for Theoretical Computer Science (EATCS), the Sociedade Brasileira de Computacao (SBC), and the Sociedade Brasileira de Logica (SBL). PAPER SUBMISSION Contributions are invited on all pertinent subjects, with particular interest in cross-disciplinary topics. Typical but not exclusive areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection. Proposed contributions should be in English, and consist of a scholarly exposition accessible to the non-specialist, including motivation, background, and comparison with related works. They must not exceed 10 pages (in font 10 or higher), with up to 5 additional pages for references and technical appendices. The paper's main results must not be published or submitted for publication in refereed venues, including journals and other scientific meetings. It is expected that each accepted paper be presented at the meeting by one of its authors. Papers must be submitted electronically at www.cin.ufpe.br/~wollic/wollic2007/instructions.html A title and single-paragraph abstract should be submitted by February 23, and the full paper by March 2 (firm date). Notifications are expected by April 13, and final papers for the proceedings will be due by April 27 (firm date). PROCEEDINGS Proceedings, including both invited and contributed papers, will be published in advance of the meeting. Publication venue TBA. INVITED SPEAKERS: TBA STUDENT GRANTS ASL sponsorship of WoLLIC'2007 will permit ASL student members to apply for a modest travel grant (deadline: April 1, 2007). See www.aslonline.org/studenttravelawards.html for details. IMPORTANT DATES February 23, 2007: Paper title and abstract deadline March 2, 2007: Full paper deadline (firm) April 12, 2007: Author notification April 26, 2007: Final version deadline (firm) PROGRAM COMMITTEE Samson Abramsky (U Oxford) Michael Benedikt (Bell Labs) Lars Birkedal (ITU Copenhagen) Andreas Blass (U Michigan) Thierry Coquand (Chalmers U, Goteborg) Jan van Eijck (CWI, Amsterdam) Marcelo Finger (U Sao Paulo) Rob Goldblatt (Victoria U, Wellington) Yuri Gurevich (Microsoft Redmond) Hermann Haeusler (PUC Rio) Masami Hagiya (Tokyo U) Joseph Halpern (Cornell U) John Harrison (Intel UK) Wilfrid Hodges (U London/QM) Phokion Kolaitis (IBM Almaden Research Center) Marta Kwiatkowska (U Birmingham) Daniel Leivant (Indiana U) (Chair) Maurizio Lenzerini (U Rome) Jean-Yves Marion (LORIA Nancy) Dale Miller (Polytechnique Paris) John Mitchell (Stanford U) Lawrence Moss (Indiana U) Peter O'Hearn (U London/QM) Prakash Panangaden (McGill, Montreal) Christine Paulin-Mohring (Paris-Sud, Orsay) Alexander Razborov (Steklov, Moscow) Helmut Schwichtenberg (Munich U) Jouko Vaananen (U Helsinki) ORGANISING COMMITTEE Marcelo da Silva Correa (U Fed Fluminense) Renata P. de Freitas (U Fed Fluminense) Ana Teresa Martins (U Fed Ceara') Anjolina de Oliveira (U Fed Pernambuco) Ruy de Queiroz (U Fed Pernambuco, co-chair) Petrucio Viana (U Fed Fluminense, co-chair) WEB PAGE www.cin.ufpe.br/~wollic/wollic2007

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from the n-category cafe'
by jim stasheff 16 Sep '06

16 Sep '06

http://golem.ph.utexas.edu/category/2006/09/groupoids_and_stacks_in_physic.… Groupoids and Stacks in Physics and Geometry Posted by John Baez MathML-enabled post (click for more details). From January 8th to April 6th of 2007, the Institut Henri Poincaré will be running a program on: * Groupoids and Stacks in Physics and Geometry If you don’t know about groupoids and stacks, or even if you do, try this overview of the subject. MathML-enabled post (click for more details). The program on Groupoids and Stacks in Physics and Geometry will feature the following workshops: * Higher structures in geometry and physics (Jan 15-Jan 19) Organizers: Alberto Cattaneo and Ping Xu * Quantum cohomology of stacks and string theory (Feb 12-Feb 16) Organizers: Kai Behrend, Barbara Fantechi and Andrew Kresch * Groupoids in operator algebras and noncommutative geometry (Feb 26-Mar 2) Organizers: Jean Renault and Jean-Louis Tu There will also be a number of long courses, including: * Kai Behrend and Andrew Kresch, Introduction to stacks * Lawrence Breen, Categorical Structures and cohomology * Jean-Louis Tu, Operator Algebras, K-theory and groupoids (abstract)(résumé) * Ping Xu, Lie groupoids and Poisson geometry (abstract) Some support is available for grad students to attend - see the program website. Posted at September 13, 2006 8:30 AM UTC

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Milan Workshop in Categorical algebra, second announcement
by S. Mantovani 15 Sep '06

15 Sep '06

********************************************** INTERNAL ACTIONS and INTERNAL STRUCTURES * WORKSHOP in CATEGORICAL ALGEBRA * ********************************************** Second announcement Dear Colleagues, the Workshop will be held at the Department of Mathematics of the Università degli Studi of Milan, from 26th to 28th of October, 2006. The purpose of the workshop is to consider the notion of internal action in different categorical contexts and to relate it with internal structures defined thereby. In particular, the well established context of semiabelian categories provides a natural setting for studying the interplay between categorical and algebraic aspects of actions, with respect to internal structures that may be defined. The workshop is intended to reflect its etymology, in order to give the participants a fruitful opportunity of debate and exchange experiences about the subject. NEWS: The web pages http://users.mat.unimi.it/users/mantovani/workshopMi06.htm have been updated and now they include: - an online inscription form to partecipate to the workshop - abstracts of the lectures - maps, logistics and directions Furthermore, it is still possible to submit contributions on related topics. For any question, please contact the organizers at milanworkshop.06(a)gmail.com Best regards, Stefano Kasangian Sandra Mantovani Beppe Metere -- Sandra Mantovani Dipartimento di Matematica Via C. Saldini, 50 20133 Milano Tel 02 50316137 Fax 02 50316090 Sandra.Mantovani(a)mat.unimi.it http://users.mat.unimi.it/~mantovani

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PSSL84, second announcement
by J=FCrgen Koslowski 15 Sep '06

15 Sep '06

PERIPATETIC SEMINAR ON SHEAVES AND LOGIC 84th meeting - second announcement Dear Colleagues, As most of you will already know, the 84th meeting of the seminar=3D20 takes place at the Department of Theoretical Computer Science of the Technical University Braunschweig, Germany, over the weekend of October 14-15, 2006. As always, the seminar welcomes talks using or addressing category theory or logic, either explicitly or implicitly, in the study of any aspect of mathematics or science. Samson Abramsky and Bob Coecke have agreed to give a series of three lectures on catgorical aspects of quantum informatics. In addition, we can now confirm the participation of professor Reinhard Werner, mathematical physicist at the TU Braunschweig with special interest in this field. Braunschweig is located about 60 km East of Hannover and about 200 km West of Berlin. It can easily be reached by car or train. The closest airport is in Hannover; the train to Hannover's main station takes about 20 minutes, and the train from there to Braunschweig takes about 40 minutes. Further information on the location of the seminar, along with details on local travel together with an online registration form can be found at =09http://www.iti.cs.tu-bs.de/TI-INFO/koslowj/PSSL84.html You will also find links to two hotels offering special university rates, but you should register by the end of September. Best regards, Jiri Adamek J=3DFCrgen Koslowski Stefan Milius --=3D20 Juergen Koslowski If I don't see you no more on this world ITI, TU Braunschweig I'll meet you on the next one koslowj(a)iti.cs.tu-bs.de and don't be late! http://www.iti.cs.tu-bs.de/~koslowj Jimi Hendrix (Voodoo Child, SR)

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