January 2007 - 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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Max
by Ross Street 02 Feb '07

02 Feb '07

I have very sad news for the categorical community. Max Kelly died yesterday 26 January 2007. I believe it was a heart attack. Ross

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Letter to Max
by joyal.andre＠uqam.ca 01 Feb '07

01 Feb '07

Dear Max, I feel deeply sad that you have left. Now that you are gone, I realise how much you mean to me. I regret not telling you that. I wish to repair that by writing you this letter. If I send it to Imogen and to your friends, it will reach you in some way. Your work has been a constant source of inspiration for me. It combines beauty, rigor and depth. It is fundamental, I use it every day. It will last forever. You were a great mathematician. I also want to thank you for inviting me to Australia. I did some of my best work there. You were a great host. I made many friends. I wish we could meet again. I will talk with you in my dreams. Yours, Andre

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Address change reminder
by Fred E.J. Linton 31 Jan '07

31 Jan '07

I've just become aware that some folks may still believe, in error, that some variation of the now defunct e-mail address 0004142427/FEJLINTON(a)MCIMAIL.COM remains valid for me (perhaps name only, or number only, w/ or w/o leading zeros). Please be aware that, as of the end of 30 June 2003, MCI Mail ceased to exist, the restructuring of MCI/WorldCom having cut off its life-support. Instead, please use my university e-mail address, which is FLinton(a)Wesleyan.edu , or the secondary, back-up, address: fejlinton(a)usa.net . Many thanks. -- Fred Linton ---

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Max Kelly; Funeral Notice
by Ross Street 31 Jan '07

31 Jan '07

Sydney Morning Herald (Wed 31 Jan 2007) Funeral Notice KELLY, Gregory Maxwell (Max) Professor. — January 26, 2007, suddenly, late of Pymble. Dearly loved husband of Imogen, loving father of Dominic, Martin, Catherine, Simon and father-in-law of Narrelle, Leisa, Albert and Cathryn. Devoted grandfather of Caitlin, Tara, Zachary, James, Vanessa, Jacob, Rebecca, Sinead, Morgan and Madison. Loving brother of Michael, fond cousin of Frieda. A Requiem Mass for MAX will be celebrated at St. Anthony in the Field Catholic Church, Myoora Road, Terry Hills, on Friday (February 2, 2007), commencing at 1 p.m. At the conclusion of the Mass, the cortege will proceed to Macquarie Park Cemetery. No flowers by request, donations may be made to The Macular Degeneration Foundation 447 Kent Street, Sydney 2000. www.mdfoundation.com.au MAURER Funeral Directors 9413 1377

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@CaT seminar - reminder
by pare＠mathstat.dal.ca 30 Jan '07

30 Jan '07

>>From pare Sun Jan 28 09:50:50 2007 Subject: @CaT seminar To: atcat Date: Sun, 28 Jan 2007 09:50:50 -0400 (AST) X-Mailer: ELM [version 2.5 PL7] Content-Length: 277 @CAT Tuesday January 30, 2007 2:30-3:30 Colloquium Room Richard Wood More on Profunctors

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ETAPS 2007: Call for Participation
by =3D?ISO-8859-1?Q?Jo=3DE3o?=3D Saraiva 30 Jan '07

30 Jan '07

***************************************************************** *** *** *** ETAPS 2007 *** *** March 24 - April 1, 2007 *** *** Braga, Portugal *** *** *** *** http://www.di.uminho.pt/etaps07/ *** *** *** *** CALL FOR PARTICIPATION *** *** *** *** Early Registration Deadline: 12th February, 2007 *** *** *** ***************************************************************** The European Joint Conferences on Theory and Practice of Software (ETAPS) is the primary European forum for academic and industrial researchers working on topics related to Software Science. It is a confederation of five main conferences, several satellite workshops and other events. ETAPS 2007 is taking place in Braga, Portugal. Braga, capital of the Minho province, is an ancient city in the heart of the green and fertile region known as the Costa Verde. The region is known for its attractiveness in terms of climate, gastronomy, prices, and culture. Braga is known for its barroque churches and splendid 18th century houses. The old city is solemn and antique, but animated with commercial activity and academic life. =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D 5 Conferences - 18 Satellite Workshops - 3 Tutorials - Tool Demonstrations =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D ------------------------------------------------------------------------- Main Conferences ------------------------------------------------------------------------- CC 2007: International Conference on Compiler Construction http://cc2007.cs.brown.edu/ ESOP 2007: European Symposium on Programming http://rap.dsi.unifi.it/esop07/ FASE 2007: Fundamental Approaches to Software Engineering http://fase07.di.fc.ul.pt FOSSACS 2007: Foundations of Software Science and Computation Structures http://www2.in.tum.de/~seidl/fossacs07/ TACAS 2007: Tools and Algorithms for the Construction and Analysis of Systems http://www.doc.ic.ac.uk/tacas07/ ----------------------------------------------------------------------- Invited Speakers ----------------------------------------------------------------------- ETAPS 2007: Rance Cleaveland - University of Maryland, USA ETAPS 2007: Bertrand Meyer - ETH Z=C3=BCrich, Switzerland CC 2007: Don Batory - University of Texas at Austin, USA ESOP 2007: Andrew Pitts - Cambridge University, UK FASE 2007: Jan Bosch - Nokia, Finland FOSSACS 2007: Radha Jagadeesan - DePaul University, USA TACAS 2007: K. Rustan M. Leino - Microsoft Research, USA Further invited speakers are giving talks in the satellite workshops. ----------------------------------------------------------------------- Satellite Workshops ----------------------------------------------------------------------- ACCAT: Applied and Computational Category Theory http://tfs.cs.tu-berlin.de/workshops/accat2007/ AVIS: Int. Workshop on Automated Verification of Infinite-State Systems http://chacs.nrl.navy.mil/AVIS07 Bytecode: Bytecode Semantics, Verification, Analysis and Transformation http://www.sci.univr.it/~spoto/Bytecode07/ COCV: Sixth Workshop on Compiler Optimization Meets Compiler Verification http://pes.cs.tu-berlin.de/cocv2007/ FESCA: Formal Foundations of Embedded Software and Component-Based Software Architectures http://palab.dcs.kcl.ac.uk/fesca/ FinCo: Foundations of Interactive Computation http://www.cs.brown.edu/sites/finco07/ GT-VMT: Int. Workshop on Graph Transformation and Visual Modeling Techniques http://www.cs.le.ac.uk/events/GTVMT07/ HAV: Heap Analysis and Verification http://www.cs.tau.ac.il/~msagiv/hav.html HFL: Hardware design using Functional Languages http://hfl07.hflworkshop.org/ LDTA: Seventh Workshop on Language Descriptions, Tools and Applications http://www.di.uminho.pt/ldta07 MBT: Third Workshop on Model Based Testing http://react.cs.uni-sb.de/mbt2007/ MOMPES: Model-based Methodologies for Pervasive and Embedded Software http://www.di.uminho.pt/mompes OpenCert: Foundations and Techniques for Open Source Software Certification http://opencert.iist.unu.edu/ QAPL: Fifth Workshop on Quantitative Aspects of Programming Languages http://www.cse.yorku.ca/qapl07 SC: Software Composition http://ssel.vub.ac.be/sc2007 SLA++P: Model-driven High-level Programming of Embedded Systems http://web.uni-bamberg.de/wiai/gdi/SLAP07/ TERMGRAPH: Fourth International Workshop on Computing with Terms and Graphs http://www.termgraph.org.uk WITS: Seventh Workshop on Issues in the Theory of Security http://www.dsi.unive.it/IFIPWG1_7/wits2007.html ----------------------------------------------------------------------- Tutorials ----------------------------------------------------------------------- Program Transformation with Stratego/XT Martin Bravenboer (Utrecht University) and Eelco Visser (Delft University of Technology) Beyond the Generators: Practical Techniques for Real-World Software Generation Anthony M. Sloane (Macquarie University) Mobility, Ubiquity, and Security Gilles Barthe (INRIA), David Pichardie (IRISA), David Aspinall (Univ. of Edinburgh), Peter M=C3=BCller (ETH Zurich), Lennart Beringer (LMU Munich) and Joe Kiniry (UC Dublin) ----------------------------------------------------------------------- Tool Demonstrations ----------------------------------------------------------------------- Demonstrations of tools presenting advances on the state of the art have been selected and are integrated in the programmes of the main conferences. ----------------------------------------------------------------------- Registration and Contact Details ----------------------------------------------------------------------- For online registration, please visit http://www.di.uminho.pt/etaps07/ and go to menu item "Registration". Contact details are available at the menu item "Contact us". In case of any questions not addressed on the web pages, please email etaps07(a)di.uminho.pt.

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Max Kelly, a master of coherence
by rjwood＠mathstat.dal.ca 30 Jan '07

30 Jan '07

We would like to add to Bill and Eduardo's letters also our feelings of deep sadness at Max's death. Max Kelly's Last Work ===================== In due course Max's last work will appear in a four-author paper. While it is not usual for coauthors to divulge who contributed what to a paper the present circumstances seem to warrant such, as an appreciation of Max's extraordinary talents and tenacity. Carboni, Kelly, Walters, and Wood, [CKWW] have for some time been extending the Carboni and Walters notion of `cartesian bicategory' to the general case of bicategories that are not necessarily locally ordered. A cartesian bicategory B ultimately has a tensor product, a pseudofunctor *:BxB--->B that is naively associative and unitary. It is natural to ask whether such (B,*) is a monoidal bicategory, in other words a one-object tricategory in the sense of [Coherence for Tricategories; Gordon, Power, and Street]=[GPS]. Early in 2005 [CKWW] had shown that _if_ a bicategory A with finite `products' -x- and 1, in the bilimit sense, has (A,x) a monoidal bicategory then a cartesian bicategory B has (B,*) monoidal. In the course of polishing the paper it came to Max's attention that nobody had _proved_ the Theorem: A bicategory with finite products is monoidal. Nobody doubted the truth of this. In fact, experts in higher dimensional category theory said that if it were not true then the definition of tricategory is wrong! But when you consider the rather large amount of data that must be assembled and the many equations (some merely implicit in words such as pseudonatural and modification) that must be verified from the apparently rather weak universal property of finite products in the bilimit sense, it seemed like a rather thankless task to write out the details. This was to Max a completely unacceptable state of affairs. If nobody doubts the statement then it must be possible to find a good proof! Now Max had no intention of redrawing any of the diagrams in [GPS]. For the last few years Max, with little central vision left as a result of macular degeneration, has been doing Mathematics using an 8-fold magnification monitor. This allowed him to see only a few square centimetres of a page at a time. Many [GPS] diagrams consume an entire page. His proof, that we were privileged to receive in the last few weeks, has _no_ diagrams (though doubtless we will incorporate a few in a publishable version of the paper). Max attributed the key idea in his proof to Ross Street. Briefly, this is how it goes: For X a finite family of objects in the bicategory A, write A(X) for the bicategory of product cones over X. Thus an object of A(X) consists of an object b of A, together with a family of arrows p_i:b--->X_i, such that for all a, the induced functor A(a,b)--->\Pi A(a,X_i) is an equivalence of categories. Lemma: !:A(X)--->1 is a biequivalence (Recall that to say B--->1 is a biequivalence is to say that: i) there is an object b in B ii) for any objects c and d in B, there is an arrow f:c--->d iii) for any arrows g,h:c--->d in B, there is a unique 2-cell g--->h. It follows that in a bicategory biequivalent to 1, every arrow is an equivalence and every 2-cell is an isomorphism.) Next, Max observes that if A has finite products then, for any B, the bicategory [B,A] of pseudofunctors, pseudonatural transformations, and modifications also has finite products, given `pointwise' by the products of A. -x- is an object of [A^2,A]. We can use (a x b) x c and a x (b x c) as names for objects in [A^3,A] and applying the Lemma to [A^3,A](a,b,c) deduce the existence of the associator equivalence, pseudonatural in a,b, and c. The associator gives rise to two arrows (abbreviating somewhat) ((ab)c)d ===> a(b(cd)) in [A^4,A](a,b,c,d) and between these we have a unique invertible modification, the \pi of [GPS]. The coherence of \pi is chiefly the Stasheff non-abelian 4-cocycle condition (again see [GPS]) and for this we need only apply the Lemma to [A^5,A](a,b,c,d,e) to see that the two modifications in question are equal. Of course the other data and equations are handled with similar appeals to the Lemma. Max was not content to stop here. In his last few days he had been learning the rather subtle definition of _symmetric_ monoidal bicategory and constructed the requisite braiding equivalence and syllepsis isomorphism for a bicategory with finite products. Everything follows from the universal property but Max has shown us _how_ so that we can calculate with these things. His insights show us the way to deal with coherence issues arising from birepresentability generally and weak n-representability when the need arises. Max's personal copy of [GPS] was autographed by Ross with the words ``To Max Kelly, a master of coherence''. Yes, he was. Aurelio Carboni, Robert Walters, and Richard Wood

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terminology
by Eduardo Dubuc 28 Jan '07

28 Jan '07

hello: Given a set CC of objects in a topos EE, consider the following property: " X no= empty iff exists C \in CC, hom(C, X) no= empty " example; CC = a set of generators Has (this property) already a name ? If not, can you suggest one ? Any answer will be welcome. (Notice that if CC is a set of points (instead of objects) we say that there are enough points) Thanks Eduardo J. Dubuc

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WoLLIC'2007 - CfP
by ruy＠cin.ufpe.br 27 Jan '07

27 Jan '07

[** 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: Springer's Lecture Notes in Computer Science. INVITED SPEAKERS: Veronique Cortier (LORIA Nancy) Martin Escardo (Birmingham) Georg Gottlob (Oxford) Achim Jung (Birmingham) Louis Kauffman (U Illinois Chicago) Sam Lomonaco (U Maryland Baltimore) Paulo Oliva (London/QM) John Reif (Duke) Yde Venema (Amsterdam) 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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