December 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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heroprichten
by mas013＠bangor.ac.uk 31 Dec '07

31 Dec '07

Dear All, or at least all who know Flemish or Dutch. I have been trying to understand / translate part of a thesis in Flemish and have come upon a word (in the context of fibred categories) that my online dictionaries cannot handle at all. It seems to be a current word in the languages as Google turns up lots of hits but none gives me enough of an idea of a more or less equivalent English or French word. The word is heroprichten Can any one help? To all and sundry categorical, Happy New Year Tim Porter

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LICS 2008 - Revised Submission Deadlines
by Kreutzer + Schweikardt 30 Dec '07

30 Dec '07

LOGIC in COMPUTER SCIENCE (LICS) 2008 The LICS 2008 submission site is now open. Submission instructions along with a link to the LICS 2008 submission site can be found at http://www.cs.cmu.edu/~fp/lics08. Revised submission deadlines: - Paper registration deadline (with short abstracts): 14 January 2008 - Paper submission deadline: 21 January 2008 LICS 2008 will be held in Pittsburgh, Pennsylvania, June 24 - 27, 2008.

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CiE08 - Final Call for Papers
by cat-dist＠mta.ca 21 Dec '07

21 Dec '07

Computability in Europe 2008: Logic and Theory of Algorithms University of Athens, June 15-20 2008 http://www.cs.swan.ac.uk/cie08/ PAPER SUBMISSION is now OPEN: http://www.cs.swan.ac.uk/cie08/submission.php SUBMISSION DEADLINE: January 4th, 2008 CiE 2008 is the fourth in a series of conferences organised by CiE (Computability in Europe), a European network of mathematicians, logicians, computer scientists, philosophers, physicists and others interested in new developments in computability and their underlying significance for the real world. Previous meetings took place in Amsterdam (2005), Swansea (2006) and Siena (2007). CiE 2008 aims at bridging the gap from the logical methods of mathematical and meta-mathematical flavour to the applied and industrial questions that are involved in devising and choosing the right algorithms and analysing their effectiveness and efficiency. TUTORIALS will be given by: John V. Tucker (Swansea) Moshe Y. Vardi (Houston, TX) PLENARY SPEAKERS will include: Keith Devlin (Stanford, CA) Rosalie Iemhoff (Utrecht) Antonina Kolokolova (Vancouver, BC) Janos Makowsky (Haifa) Dag Normann (Oslo) Prakash Panangaden (Montreal, QC) Christos Papadimitriou (Berkeley, CA) Jan van Leeuwen (Utrecht) & Jiri Wiedermann (Prague) See http://www.cs.swan.ac.uk/cie08/invited.php for more informations on Plenary Speakers. SPECIAL SESSIONS Algorithms in the history of mathematics (organized by J. Hoyrup, Roskilde, and K. Chemla, Paris) Formalising mathematics and extracting algorithms from proofs (organized by H. Barendregt, Nijmegen, and M. Seisenberger, Swansea) Higher type recursion theory and applications (organized by U. Berger, Swansea, and D. Normann, Oslo) Algorithmic game theory (organized by E. Koutsoupias, Athens, and B. von Stengel, London) Quantum algorithms and complexity (organized by V. Kendon, Leeds, and B. Coecke, Oxford) Biology and computation (organized by N. Jonoska, Tampa FL, and G. Mauri, Milano) See http://www.cs.swan.ac.uk/cie08/special.php for more informations on special sessions. CiE 2008 conference topics include, but not exclusively * Admissible sets * Analog computation * Artificial intelligence * Automata theory * Classical computability and degree structures * Complexity classes * Computability theoretic aspects of programs * Computable analysis and real computation * Computable structures and models * Computational and proof complexity * Computational learning and complexity * Concurrency and distributed computation * Constructive mathematics * Cryptographic complexity * Decidability of theories * Derandomization * DNA computing * Domain theory and computability * Dynamical systems and computational models * Effective descriptive set theory * Finite model theory * Formal aspects of program analysis * Formal methods * Foundations of computer science * Games * Generalized recursion theory * History of computation * Hybrid systems * Higher type computability * Hypercomputational models * Infinite time Turing machines * Kolmogorov complexity * Lambda and combinatory calculi * L-systems and membrane computation * Mathematical models of emergence * Molecular computation * Neural nets and connectionist models * Philosophy of science and computation * Physics and computability * Probabilistic systems * Process algebra * Programming language semantics * Proof mining * Proof theory and computability * Quantum computing and complexity * Randomness * Reducibilities and relative computation * Relativistic computation * Reverse mathematics * Swarm intelligence * Type systems and type theory * Uncertain reasoning * Weak systems of arithmetic and applications Contributed papers will be selected from submissions received by the PROGRAMME COMMITTEE consisting of: L. Aiello (Roma) T. Altenkirch (Nottingham) K. Ambos-Spies (Heidelberg) G. Ausiello (Roma) A. Beckmann (Swansea, co-chair) L. Beklemishev (Moscow) P. Bonizzoni (Milano) S. A. Cook (Toronto ON) B. Cooper (Leeds) C. Dimitracopoulos (Athens, co-chair) R. Downey (Wellington) E. Koutsoupias (Athens) O. Kupferman (Jerusalem) S. Laplante (Orsay) H. Leitgeb (Bristol) B. Loewe (Amsterdam) E. Mayordomo Camara (Zaragoza) F. Montagna (Siena) M. Mytilinaios (Athens) (+) M. Nielsen (Aarhus) I. Oitavem (Lisboa) C. Palamidessi (Palaiseau) T. Pheidas (Heraklion) Ramanujam (Chennai) A. Schalk (Manchester) U. Schoening (Ulm) H. Schwichtenberg (Muenchen) A. Selman (Buffalo NY) A. Sorbi (Siena) I. Soskov (Sofia) C. Timpson (Leeds) S. Zachos (New York NY) We cordially invite all researchers (European and non-European) in computability related areas to submit their papers (in PDF- format, max 10 pages) for presentation at CiE 2008. We particularly invite papers that build bridges between different parts of the research community. The CONFERENCE PROCEEDINGS will be published by LNCS, Springer-Verlag. There will also be journal special issues, collecting invited contributions related to the conference. Special issues will be published in the journals "Theory of Computing Systems", the "Archive for Mathematical Logic", and the "Journal of Algorithms". See http://www.cs.swan.ac.uk/cie08/publications.php for more informations on publications.

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On defining *-autonomous categories
by Michael Barr 20 Dec '07

20 Dec '07

I got a note from a student named Benjamin Jackson saying that someone had told him that to define a *-autonomous category, you need only a symmetric monoidal category and a contravariant involution * such that Hom(A @ B,C*) = Hom(A,(B @ C)*). Here "=" means natural equivalence and @ is the tensor product. Not only is this apparently true but that equivalence is needed only for A = I, the tensor unit. Of course, what is going on is that all the coherence is built-in to the structure of a symmetric monoidal category. First define A --o B = (A @ B*)*. Then the isomorphism above implies that Hom(A,B) = Hom(I @ A,B) = Hom(I,(A @ B*)*) = Hom(I,A --o B) Next we see that (A @ B) --o C = (A @ B @ C*)* = A --o (B @ C*)* = A --o (B --o C) and, applying Hom(I,-), that Hom(A @ B,C) = Hom(A,B --o C) Also we have that A --o I* = (A @ I)* = A* and A --o B = (A @ B*)* = (B* @ A)* = B* --o A* which gives the structure of a *-autonomous category with dualizing object I*. The trouble with this is that generally speaking it is the --o which is obvious and the tensor is derived from it. The coherences involving internal hom alone are much less well-known, although they are included in the original Eilenberg-Kelly paper in the La Jolla Proceedings. Still I am surprised that I never noticed this before.

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CFP ICGT'08: The 4th Intl. Conference on Graph Transformation, 7 - 13 Sept 2008, Leicester (UK)
by Reiko Heckel 19 Dec '07

19 Dec '07

Call for Papers ----------------------------------------------------------------- 4th International Conference on Graph Transformation (ICGT 2008) Leicester, United Kingdom, September 7 - 13, 2008, http://www.cs.le.ac.uk/events/icgt2008/ ----------------------------------------------------------------- The 4th International Conference on Graph Transformation (ICGT 2008) will be held in Leicester (United Kingdom) in the second week of September 2008, along with several satellite events. It continues the line of conferences previously held in Barcelona (Spain) in 2002, Rome (Italy) in 2004, and Natal (Brazil) in 2006 as well as a series of six International Workshops on Graph Transformation with Applications in Computer Science between 1978 and 1998, and alternates with the workshop series on Application of Graph Transformation with Industrial Relevance. The conference takes place under the auspices of EATCS, EASST, and IFIP WG 1.3. Awards will be given by EATCS and EASST for the best theoretical and application-oriented papers. Proceedings are planned with Springer's Lecture Notes in Computer Science series. ----------------------------------------------------------------- Scope of the Conference: Graphs are among the simplest and most universal models for a variety of systems, not just in computer science, but throughout engineering and the life sciences. When systems evolve we are interested in the way they change, to predict, support, or react to their evolution. Graph transformation combines the idea of graphs as a universal modelling paradigm with a rule-based approach to specify evolution. The area is concerned with both the theory of graph transformation and their application to a variety of domains. The conference aims at bringing together researchers and practitioners interested in the foundations and application of graph transformation to a variety of areas. Topics of interest include, but are not limited to * foundations and theory of o General models of graph transformatio o High-level and adhesive replacement systems o Node-, edge-, and hyperedge replacement grammars o Parallel, concurrent, and distributed graph transformations o Term graph rewriting o Hierarchical graphs and decompositions of graphs o Logic expression of graph transformation properties o Graph theoretical properties of graph languages o Geometrical and topological aspects of graph transformation o Automata on graphs and parsing of graph languages o Analysis and verification of graph transformation systems o Structuring and modularization concepts for transformation systems o Graph transformation and Petri nets * application to, languages and tool support for o Software architecture o Workflows and business processes o Software quality and testing o Software evolution o Access control and security models o Aspect-oriented development o Model-driven development, especially model transformations o Domain-specific languages o Implementation of programming languages o Bioinformatics and system biology o Natural computing o Image generation and pattern recognition techniques o Massively parallel computing o Self-adaptive systems and ubiquitous computing o Service-oriented applications and semantic web o Rule- and knowledge-based systems ------------------------------------------------------------------ Keynote speakers: Wil van der Aalst, Eindhoven University of Technology Heiko Dörr, Carmeq GmbH, Berlin Perdita Stevens, University of Edinburgh ------------------------------------------------------------------ Satellite Events: Doctoral Symposium Contact: Andrea Corradini <andrea(a)di.unipi.it> GCM: Workshop on Graph Computation Models Contact: Mohamed Mosbah <mosbah(a)labri.fr> GraBaTs: Graph Transformation Tools Contest Contact: Arend Rensink <rensink(a)cs.utwente.nl> Tutorial: Introduction to Graph Transformation Contact: Reiko Heckel <reiko(a)mcs.le.ac.uk> PNGT: Petri Nets and Graph Transformations Contact: Paolo Baldan <baldan(a)dsi.unive.it> NCTG: Natural Computing and Graph Transformation Contact: Grzegorz Rozenberg <rozenber(a)liacs.nl>, Ian Petre <ipetre(a)abo.fi> ------------------------------------------------------------------ Submissions: Submitted papers should not exceed fifteen (15) pages using Springer's LNCS format, and should contain original research. Simultaneous submission to other conferences with proceedings or submission of material that has already been published elsewhere is not allowed. ------------------------------------------------------------------ Important Dates: Submission of title and abstract: April 10, 2008 Submission of complete paper: April 17, 2008 Notification of acceptance: May 15, 2008 Final version due: June 15, 2008 Main conference: September 10-12, 2008 Conference (with satellite events): September 7-13, 2008 ------------------------------------------------------------------ Venue: Located in the heart of England, Leicester is a truly multi-cultural city. The city is a historic meeting place, where for centuries people of different races and cultures have gathered, creating a rich and unique heritage. This diversity continues today with a thriving ethnic minority community accounting for more than a third of Leicester's population. ICGT 2008 will be held at the University of Leicester's conference facility next to the Universiy's botanic gardens. ------------------------------------------------------------------ Organisation Program Chairs Reiko Heckel <reiko(a)mcs.le.ac.uk>, University of Leicester, United Kingdom Gabriele Taentzer <taentzer(a)mathematik.uni-marburg.de>, Philipps-Universität Marburg, Germany Local Organisation Reiko Heckel <reiko(a)mcs.le.ac.uk>, University of Leicester, United Kingdom Publicity Chair: Karsten Ehrig <karsten(a)mcs.le.ac.uk>, University of Leicester, United Kingdom Workshop Chair: Dénes Bisztray <dab24(a)mcs.le.ac.uk>, University of Leicester, United Kingdom ------------------------------------------------------------------ PC members: # Paolo Baldan, Padova (Italy) # Luciano Baresi, Milano (Italy) # Michel Bauderon, Bordeaux (France) # Andrea Corradini, Pisa (Italy) # Hartmut Ehrig, Berlin (Germany) # Gregor Engels, Paderborn (Germany) # Annegret Habel, Oldenburg (Germany) # Reiko Heckel (co-chair), Leicester (UK) # Dirk Janssens, Antwerp (Belgium) # Garbor Karsai, Nashville (USA) # Barbara Koenig, Stuttgart (Germany) # Hans-Jörg Kreowski, Bremen (Germany) # Juan de Lara, Madrid (Spain) # Tom Mens, Mons (Belgium) # Mark Minas, München (Germany) # Ugo Montanari, Pisa (Italy) # Mohamed Mosbah, Bordeau (France) # Manfred Nagl, Aachen (Germany) # Fernando Orejas, Barcelona (Spain) # Francesco Parisi-Presicce, Rome (Italy) # Mauro Pezzè, Milano (Italy) # John Pfaltz, Charlottesville (Virginia, USA) # Rinus Plasmeijer, Nijmegen (The Netherlands) # Detlef Plump, York (UK) # Arend Rensink, Twente (The Netherlands) # Leila Ribeiro, Porto Alegre (Brasil) # Grzegorz Rozenberg, Leiden (The Netherlands) # Andy Schürr, Darmstadt (Germany) # Gabriele Taentzer (co-chair), Marburg (Germany) # Hans Vangheluwe, Montreal (Canada) # Dániel Varró, Budapest (Hungary) # Albert Zündorf, Kassel (Germany) -- Prof Dr Reiko Heckel Chair of Software Engineering Department of Computer Science University of Leicester Leicester LE1 7RH United Kingdom Tel +44 (0)116 252 3406 Fax +44 (0)116 252 3915 http://www.cs.le.ac.uk/people/rh122

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A meeting in honour of Bill Lawvere, Como, 10 January 2008 - for the categories list
by RFC Walters 19 Dec '07

19 Dec '07

-------------------------------------- A meeting in honour of Bill Lawvere -------------------------------------- Como (Italy), January 10, 2008 An informal meeting will be held at the University of Insubria in Como to celebrate the 70th birthday of Bill Lawvere. The meeting will consist in a series of three lectures entitled "Cohesive toposes: combinatorial and infinitesimal cases" given by Bill Lawvere, a round table and a social dinner. If you would like to attend the dinner please contact me at robert.walters(a)uninsubria.it Further details of the meeting will be made available at http://dscpi.uninsubria.it/staff/Walters/Como_Category_Seminar Bob Walters 19th December 2007

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Re: new website: clones and genoids
by Zhaohua Luo 19 Dec '07

19 Dec '07

Thanks for the comments. Zack Luo -----Original Message----- From: Peter Selinger [mailto:selinger@mathstat.dal.ca] Sent: Monday, December 10, 2007 8:22 PM To: Zhaohua Luo Subject: Re: categories: new website: clones and genoids By "itself", do you mean A or G? Grammatically, I would understand "the product of A with itself" to be A x A, but then your definition does not have the stated consequences. I therefore assume that you meant "the product of A with G". Another unambiguous way to express this is "G is the product of itself with A". -- Peter Zhaohua Luo wrote: > > A genoid is a category of only two objects (A, G) such that G is the product > of A with itself (thus G is also the product of any finite power of A with > itself). It is a remarkable fact that such a simple concept can be used to > define all of the fundamental algebraic theories, including lambda calculus > and first order logic. Progress made in this direction is presented at a > newly created website entitled "Clones <http://www.algebraic.net/cag> and > Genoids" (http://www.algebraic.net/cag) > > Zhaohua Luo

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list interruption
by Bob Rosebrugh 19 Dec '07

19 Dec '07

The categories moderator will be mostly out of email contact for the period December 20-28, 2007. Postings submitted to categories during that period will be distributed by December 29. Best wishes, Bob Rosebrugh

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Question for catbul on practical use of the language of monoidal categories
by Ronnie 19 Dec '07

19 Dec '07

I would like help on an expository point when using structures such as a tensor product in a practical situation, and where one does not want to overload the reader, and make things seem more complicated than necessary. I accept the excellent example in CFTWM p.164 2nd edition that even for the cartesian product one cannot get a strict associativity isomorphism. However when dealing say with tensor product of modules over a commutative ring, one feels that the tensor product associativity is no less strict than the usual product of sets, because of the definition by the universal bilinear property, which extends to 3-fold tensor products and trilinearity. Has this feeling been clearly expressed in the literature? Again, is there an exposition of say the tensor algebra of a vector space which adequately (in your view) takes account of coherence? I am trying to finalise an account of tensor products of crossed complexes, a much more complicated situation, but where the same ideas arise. Ronnie

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