July 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 ************************************************************

2 1

definition of parsimony
by Axel Rossberg 31 Jul '07

31 Jul '07

Dear List Members, I am looking for a formal definition of parsimony for fundamental scientific theories. From the tiny bit I understood of category theory, I had the impression it might provide the right framework for such a definition. The problem of motivating and defining parsimony is being discussed in analytic philosophy. An overview over the discussion can be found at http://plato.stanford.edu/entries/simplicity/ , which starts off with the sentences Most philosophers believe that, other things being equal, simpler theories are better. But what exactly does theoretical simplicity amount to? Syntactic simplicity, or elegance, measures the number and conciseness of the theories basic principles. Ontological simplicity, or parsimony, measures the number of kinds of entities postulated by the theory. One issue concerns how these two forms of simplicity relate to one another. I am interested in the "ontological simplicity, or parsimony". However, if one understands modern physics as describing essentially only one thing, the wave-function of the universe, then even the idea of defining parsimony in terms of numbers of kinds of things seems to be a bit odd. Yet, I think the idea is intuitively clear. The minimum requirement for a formal definition of parsimony is perhaps that it should identify theories such as the dynamics of Newtonian point-particles or the current "standard model" of particle physics as parsimonious, while the same theories with some oddities added, which do not themselves affect the "real" physics, should be identifiable as non-parsimonious. Beyond this, such a definition should presuppose as little as possible about the nature of the theories it applies to. Does somebody know about applications of category theory to this problem, or have an idea for who to do it? Cheers, Axel Rossberg --- Evolution and Ecology Program International Institute for Applied Systems Analysis Schlossplatz 1 A-2361 Laxenburg AUSTRIA ++++++++++++++++++++++++ reprints http://axel.rossberg.net/paper and more http://axel.rossberg.net

2 2

correction w.r.t. generic finite family of finite objects
by Thomas Streicher 27 Jul '07

27 Jul '07

Andreas Blass has pointed out to me that that there was a mistake in my recent mail. There does exist a global element n : 1 -> N such that G \cong K_n (n is the order of the group G) BUT the statement G \cong K_n contains a hidden existential quantifier over Iso(G,K_n) and this latter one is not witnessed by a global section of Iso(G,K_n). Thomas Streicher

1 0

answer by Blass: generic family
by Thomas Streicher 26 Jul '07

26 Jul '07

A very satisfying answer to my recent question on this list has been given to me by Andreas Blass. Since \Delta : Set -> Psh(G) is logical there is no way of defining a generic family of finite objects in the language of higher order arithmetic since every such family would be of the form \Delta(u). That such a family can't be generic is shown already by the argument in my mail. Moreover, as he pointed out and I also observed, although A -> I is a family of finite sets iff \forall i:I.\exists! n:N. A_i \cong K_n there will in general be no external choice function providing such an n:N for i:I although internally by AUC there exists a unique such choice function. After all this is no suprise since the representable object of Psh(G) has global support but no global element (unless G is trivial). Thomas

1 0

CRM 2007/2008: Homotopy Theory and Higher Categories
by Joachim Kock 25 Jul '07

25 Jul '07

CRM 2007/2008: Homotopy Theory and Higher Categories This is to announce that a research programme on homotopy theory and higher categories, in a broad sense, will take place at the CRM in Barcelona during the academic year 2007-2008. The scientific organisers are Carles Casacuberta (Barcelona), Andre Joyal (Montreal), Joachim Kock (Barcelona), Amnon Neeman (Canberra), and Frank Neumann (Leicester). In addition to a weekly seminar throughout the year, the following events are scheduled: - November 5 to 14, 2007: Workshop on Derived Categories - February 4 to 14, 2008: Advanced Course on Simplicial Methods in Higher Categories - February 18 to 22, 2008: Workshop on Algebra and Geometry of Groups and Classifying Spaces - April 1 to 5, 2008: Workshop on Topological and Differentiable Stacks - June 16 to 20, 2008: Workshop on Categorical Groups - June 30 to July 5, 2008: HOCAT 2008, a conference on Homotopy Structures in Geometry and Algebra; Derived Categories, Higher Categories Participants are welcome to any of these activities. Longer-term visits are partially constrained by office space availability at the CRM. Please contact the coordinators of each activity or the CRM Secretariat if you need more information. Updated details about activities and visitors can be found on the website http://www.crm.cat/HOCAT/. With best regards, The Scientific Organisers

1 0

pivotal adjoints?
by Aaron Lauda 25 Jul '07

25 Jul '07

Dear category theorists, Suppose we have chosen left and right adjoints for F:A->B and G:A->B F-| F* -| F and G-| G*-|G i_F: 1_B => FF* i_G: 1_B => GG* e_F: F*F => 1_A e_G: G*G => 1_A j_F: 1_A => F*F j_G: 1_A => G*G k_F: FF* => 1_B k_G: GG* => 1_B Then given any 2-morphism a:F=>G there are two obvious duals (mates under adjunction) for the 2-morphsism a a+ :G*=>F* := (e_G F*).(G*aF*).(G* i_F) +a :G*=>F* := (F* k_G).(F*aG*).(j_F G*) or for those who like pictures: +a a+ __ __ / \ | | / \ | | | | | | | a | | a | | | | | | | | \__/ \__/ | | | In general a+ is not equal to +a because if is was we could always twist one of the units and counits so that it does not hold. Has the condition that a+ = +a been investigated in the literature anywhere? In particular, if a 2-category is such that all 1-morphisms F have a simultaneous left and right adjoint then has anyone studied the context where the adjoints are such that a+ = +a is always satisfied? Perhaps, this notion has been studied in the language of duals for 1-morphisms? The above condition appears to be related to the notion of pivotal category when we look at Hom(A,A) for any object A. Thanks, Aaron Lauda

2 2

Bicomma objects
by Steve Vickers 24 Jul '07

24 Jul '07

What is the difference between a bicomma object and a comma object (a.k.a. lax pullback)? Steve.

2 1

CFP: FoIKS 2008
by Markus Kirchberg 24 Jul '07

24 Jul '07

C A L L F O R P A P E R S --------------------------------- Fifth International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2008) February 11-15, 2008 -- Pisa, Italy http://2008.foiks.org/ The FoIKS symposia provide a biennial forum for presenting and discussing theoretical and applied research on information and knowledge systems. The goal is to bring together researchers with an interest in this subject, share research experiences, promote collaboration and identify new issues and directions for future research. FoIKS 2008 solicits original contributions dealing with any foundational aspect of information and knowledge systems, including submissions from researchers working in fields such as discrete mathematics, logic and algebra, model theory, information theory, complexity theory, algorithmics and computation, statistics and optimisation who are interested in applying their ideas, theories and methods to research on information and knowledge systems. Previous FoIKS symposia were held in Budapest (Hungary) in 2006, Vienna (Austria) in 2004, Schloss Salzau near Kiel (Germany) in 2002, and Burg/Spreewald near Berlin (Germany) in 2000. FoIKS took up the tradition of the conference series Mathematical Fundamentals of Database Systems (MFDBS), which initiated East-West collaboration in the field of database theory. Former MFDBS conferences were held in Rostock (Germany) in 1991, Visegrad (Hungary) in 1989, and Dresden (Germany) in 1987. The FoIKS symposia are a forum for intensive discussions. Speakers are given sufficient time to present their results, expound relevant background information and put their research into context. Furthermore, participants are asked in advance to prepare as correspondents to a contribution of another author. Suggested topics include, but are not limited to: * Database Design: formal models, dependency theory, schema translations, desirable properties; * Dynamics of Information and Knowledge Systems: models of transactions, models of interaction, updates, consistency preservation, concurrency control; * Information Integration: heterogeneous data, views, schema dominance and equivalence; * Integrity and Constraint Management: verification, validation, and enforcement of consistency, triggers; * Intelligent Agents: multi-agent systems, autonomous agents, foundations of software agents, cooperative agents; * Knowledge Discovery and Information Retrieval: machine learning, data mining, text mining, information extraction; * Knowledge Representation: planning, reasoning techniques, description logics, knowledge and belief, belief revision and update, non-monotonic formalisms, uncertainty; * Logics in Databases and AI: non-classical logics, spatial and temporal logics, probabilistic logics, deontic logic, logic programming; * Mathematical Foundations: discrete structures and algorithms, graphs, grammars, automata, abstract machines, finite model theory, information theory; * Security and Risk Management in Information and Knowledge Systems: privacy, trust, cryptography, steganography, information hiding; * Semi-Structured Data and XML: data modelling, data processing, data compression, data exchange; * Social and Collaborative Computing: symbiotic intelligence, self-organisation, knowledge flow, decision making; * The Semantic Web and Knowledge Management: languages, ontologies, agents, adaption, intelligent algorithms; and * The WWW: models of Web databases, Web dynamics, Web services, Web transactions and negotiations. SUBMISSION OF PAPERS -------------------- Papers must be typeset using the Springer-Verlag LaTeX2e style llncs for Lecture Notes in Computer Science (refer http://2008.foiks.org/) The suggested number of pages is 16, and the maximum number of pages is 18. Submissions which deviate substantially from these guidelines may be rejected without review. Initial submissions must be in PDF format, but authors should keep in mind that the LaTeX2e source must be submitted for the final versions of accepted papers. Submissions in alternate formats, such as Microsoft Word, cannot be accepted for either initial or final versions. The submissions will be judged for scientific quality and for suitability as a basis for broader discussion. The proceedings will be published by Springer-Verlag in the Lecture Notes in Computer Science series and will be available at the symposium. After the symposium authors of selected papers will be asked to prepare extended versions of their papers for publication in a special issue of the journal Annals of Mathematics and Artificial Intelligence. Electronic Submission --------------------- Submission to FoIKS 2008 will be electronically only. Authors are asked to create a submission system account first. Subsequently, this account can be used to submit one or more abstracts and upload corresponding papers. The online submission system will be available from late-July 2007. IMPORTANT DATES --------------- Abstract submission deadline: August 15, 2007 (extended) Paper submission deadline: August 22, 2007 (extended) Author notification: October 15, 2007 Camera ready paper due: November 12, 2007 Early registration due: January 31, 2008 Late registration: from February 01, 2008 Symposium in Pisa, Italy: February, 11-15 2008 CONFERENCE CHAIRS ----------------- Program Committee Co-Chairs --------------------------- Sven Hartmann Massey University, New Zealand Gabriele Kern-Isberner University of Dortmund, Germany Local Arrangements Chair ------------------------ Carlo Meghini Istituto di Scienza e Tecnologie dell'Informazione, Italy Publicity Chair --------------- Markus Kirchberg Massey University, New Zealand PROGRAM COMMITTEE ----------------- Rudolf Ahlswede, University of Bielefeld, Germany Catriel Beeri, The Hebrew University of Jerusalem, Israel Leopoldo Bertossi, Carleton University, Canada Joachim Biskup, University of Dortmund, Germany Stefan Brass, University of Halle, Germany Cristian S. Calude, University of Auckland, New Zealand John Cantwell, Royal Institute of Technology, Sweden Samir Chopra, City University of New York, USA James P. Delgrande, Simon Fraser University, Canada Juergen Dix, Clausthal University of Technology, Germany Rod Downey, Victoria University of Wellington, New Zealand Thomas Eiter, Vienna University of Technology, Austria Lluis Godo Lacasa, Institut d'Investigacioen Intel.ligencia Artificial, Spain Stephen J. Hegner, Umea University, Sweden Anthony Hunter, University College London, UK Hyunchul Kang, Chung-Ang University Seoul, Korea Odej Kao, Berlin University of Technology, Germany Gyula O. H. Katona, Hungarian Academy of Sciences, Hungary Hans-Joachim Klein, University of Kiel, Germany Dexter Kozen, Cornell University, USA Jerome Lang, Institut de Recherche en Informatique de Toulouse, France Uwe Leck, University of Wisconsin, USA Mark Levene, Birbeck University of London, UK Sebastian Link, Massey University, New Zealand Yue Lu, East China Normal University Shanghai, China Thomas Lukasiewicz, Universita di Roma "La Sapienza", Italy Carlo Meghini, Istituto di Scienza e Tecnologie dell'Informazione, Italy Peter Mika, Yahoo! Research Barcelona, Spain Wilfred S. H. Ng, Hong Kong University of Science and Technology, China Beng Chin Ooi, National University of Singapore Jeff B. Paris, University of Manchester, UK Henri Prade, Universite Paul Sabatier, France Attila Sali, Hungarian Academy of Sciences, Hungary Vladimir Sazonov, University of Liverpool, UK Klaus-Dieter Schewe, Massey University, New Zealand Karl Schlechta, Universite de Provence, France Dietmar Seipel, University of Wuerzburg, Germany Guillermo R. Simari, Universidad Nacional del Sur, Argentina Nicolas Spyratos, University of Paris-South, France Ernest Teniente, Universitat Politecnica de Catalunya, Spain Bernhard Thalheim, University of Kiel, Germany Yannis Theodoridis, University of Piraeus, Greece Miroslav Truszczynski, University of Kentucky, USA Jose Maria Turull-Torres, Massey University Wellington, New Zealand Dirk Van Gucht, Indiana University, USA Marina de Vos, University of Bath, UK Jef Wijsen, University of Mons-Hainaut, Belgium Ian H. Witten, University of Waikato, New Zealand Jeffrey Xu Yu, Chinese University of Hong Kong, China FURTHER INFORMATION ------------------- For further information refer to the FoIKS 2008 Web-site at http://2008.foiks.org/

1 0

Workshop in honour of J Adamek and W Tholen
by Categorical Methods 24 Jul '07

24 Jul '07

REGISTRATION for the Workshop Categorical Methods in Algebra, Topology and Computer Science, in honour of Jiri Adamek and Walter Tholen, to be held in Coimbra, in October 26-28, 2007, is now OPEN, at the web page http://www.mat.uc.pt/~cmatcs/ If you plan to participate, please register as soon as possible. The number of rooms in the hotels indicated in the web page is limited, so early reservations are recommended.

1 0

2nd CFP: ACM SAC Special Track on Coordination Models, Languages and Architectures
by Michael Ignaz Schumacher - CM at ACM SAC08 24 Jul '07

24 Jul '07

[Apologies if you receive multiple copies] 2nd CFP: ACM SAC Special Track on Coordination Models, Languages and Architectures ----------------------------------------------------------------------- CALL FOR PAPERS ----------------------------------------------------------------------- Coordination Models, Languages and Applications Special Track of the 23rd ACM Symposium on Applied Computing (SAC08) March 16 - 20, 2008, Fortaleza, Brazil http://ii.hevs.ch/sac2008 ----------------------------------------------------------------------- IMPORTANT DATES * Submission deadline: 7 September 2007 * Author notification: 15 October 2007 * Camera ready: 30 October 2007 ----------------------------------------------------------------------- AIMS & SCOPE Building on the success of the nine previous editions (1998-2007), a special track on coordination models, languages and applications will be held at SAC 2008. Over the last decade, we have witnessed the emergence of models, formalisms and mechanisms to describe concurrent and distributed computations and systems based on the concept of coordination. The purpose of a coordination model is to enable the integration of a number of, possibly heterogeneous, components (processes, objects, agents) in such a way that the resulting ensemble can execute as a whole, forming a software system with desired characteristics and functionalities which possibly takes advantage of parallel and distributed systems. The coordination paradigm is closely related to other contemporary software engineering approaches such as multi-agent systems, service-oriented architectures, component-based systems and related middleware platforms. Furthermore, the concept of coordination exists in many other Computer Science areas such as workflow systems, cooperative information systems, distributed artificial intelligence, and internet technologies. After more than a decade of research, the coordination paradigm is gaining increased momentum in state-of-the-art engineering paradigms such as multi-agent systems and service-oriented architectures: in the first case, coordination abstractions are perceived as essential to design and support the working activities of agent societies; in the latter case, service coordination, orchestration, and choreography are going to be essential aspects of the next generations of systems based on Web services. The Special Track on Coordination Models, Languages and Applications takes a deliberately a broad view of what constitutes coordination. Accordingly, major topics of interest this year will include: - Novel models, languages, programming and implementation techniques - Applications of coordination technologies - Industrial points of view: experiences, applications, open issues - Internet- and Web-based coordinated systems - Coordination of multi-agent systems, including mobile agents, intelligent agents, and agent-based simulations - Coordination in Service-oriented architectures and Web Services - Languages for service description and composition - Models, frameworks and tools for Group Decision Making - Modern Workflow Management Systems and Case-Handling - Coordination in Computer Supported Cooperative Work - Software architectures and software engineering techniques - Configuration and Architecture Description Languages - Coordination Middleware and Infrastructures - Coordination in GRID systems - Emergent Coordination: Swam based, Stigmergy - Coordination technologies, systems and infrastructures - Relationship with other computational models such as object oriented, declarative (functional, logic, constraint), programming or their extensions with coordination capabilities - Formal aspects (semantics, reasoning, verification) ----------------------------------------------------------------------- PROCEEDINGS AND POST-PROCEEDINGS Papers accepted for the Special Track on Coordination Models, Languages and Applications will be published by ACM both in the SAC 2008 proceedings and in the Digital Library. Selected papers will be published in a Journal's special issue. ----------------------------------------------------------------------- PAPER SUBMISSION Original papers from the above-mentioned or other related areas will be considered. This includes three categories of submissions: 1) original and unpublished research; 2) reports of innovative computing applications in the arts, sciences, engineering, business, government, education and industry; and 3) reports of successful technology transfer to new problem domains. Each submitted paper will be fully refereed and undergo a blind review process by at least three referees. The accepted papers in all categories will be published in the ACM SAC 2008 proceedings. Format: Submit your paper electronically in either PDF or postscript format. Please note: neither hardcopy nor fax submissions will be accepted. Submissions should be printable on a standard printer on common paper formats such as letter and DIN A4. Please use a Postscript previewer such as Ghostview to check the portability of Postscript documents. The author(s) name(s) and address(es) must not appear in the body of the paper, and self reference should be in the third person. This is to facilitate blind review. The body of the paper should not exceed 4,000 words. Accepted full papers should not exceed 5 pages in a double column format (with the option, at additional expense, to add three more pages). Accepted poster papers will be published as extended 2-page abstracts in the symposium proceedings. All submissions must be received by 7 September 2007 SUBMISSION PROCEDURE Submission is entirely automated by an eCMS paper management tool, which is available from the main SAC Web Site: http://www.acm.org/conferences/sac/sac2008/. Authors must first register their own account by obtaining a password, and then follow the instructions. ----------------------------------------------------------------------- PROGRAM CHAIRMEN Michael Ignaz Schumacher, Swiss Federal Institute of Technology Lausanne (EPFL) & University of Applied Sciences Western Switzerland Alan Wood, University of York, UK Email contact : cm.sac2008(a)gmail.com ----------------------------------------------------------------------- PROGRAM COMMITTEE Arbab Farhad, CWI & Leiden University, Netherlands Bonsangue Marcello, Leiden University, Netherlands Bortenschlager Manfred, Salzburg Research, Austria Chaudron Michel, Technical University of Eindhoven, Netherlands de Nicola Rocco, University of Florence, Italy Ferrari Gianluigi, University of Pisa, Italy Fiadeiro Jose, University of Leicester, UK Harrison-Broninski Keith, Role Modellers Ltd, UK Jacob Jeremy, University of York, UK Lichtner Kurt, University of Waterloo, Canada Muccini Henry, University of l'Aquila, Italy Murphy Amy, University of Lugano, Switzerland Norton Barry, University of Sheffield, UK Omicini Andrea, University of Bologna, Italy Oriol Manuel, ETH Zurich, Switzerland Pallota Vincenzo, University of Fribourg, Switzerland Petta Paolo, Medical University of Vienna, Austria Picco Gian Pietro, University of Trento, Italy Razvan Popescu, University of Pisa, Italy Andries Stam, Leiden University, Netherlands Porto Antonio, New University of Lisbon, Portugal Pugliese, Rosario, University of Florence, Italy Rossi Davide, Scienze dell'Informazione, Bologna, Italy Tahara Yasuyuki, National Institute of Informatics, Japan Talcott Carolyn, SRI International, USA Wells George, Rhodes University, South Africa Wiklicky Herbert, Imperial College London, UK Wojciechowski Pawel T., Poznan University of Technology, Poland Zambonelli Franco, University of Modena-Reggio Emilia, Italy

1 0