May 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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some Bangor preprints
by Ronnie Brown 01 Jun '06

01 Jun '06

I have put some preprints on http://www.bangor.ac.uk/~mas010/brownpr.html 1. Normalisation for the fundamental crossed complex of a simplicial set. R. Brown and R. Sivera This is but one more step in setting up crossed complexes as a basic somewhat nonabelian tool in algebraic topology. It shows how crossed complexes are used to express the homotopy addition lemma, and gives an analogue of a theorem classical for simplicial abelian groups. 2. Analogy, concepts and methodology in Mathematics. R. Brown and T. Porter This is an an article for undergraduates to appear in Eureka, Journal of the Archimideans at Cambridge. It is about rather than on mathematics. It includes two quotations from a correspondence with Grothendieck. It could be seen as relevant to the article `Mathematical Morality' by Eugenia Cheng. Other Bangor preprints are on http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/ Ronnie Brown www.bangor.ac.uk/r.brown/topgpds.html

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two topology questions
by Paul Taylor 30 May '06

30 May '06

Is there an introduction to CONTINUOUS LATTICES written specifically for (and ideally BY) real analysts? (completely unrelated:) Is there a word for a (necessarily compact) space X for which the unique map X --> 1 is a proper surjection? Maybe "occupied"? In the latter question, you may interpret "space" in any appropriate sense, for example to mean locale or topos or ASD object or formal space, or whatever you like. Paul PS See you all in Canada (Calgary & Nova Scotia) in June.

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Higher-dimensional algebra - a language for quantum spacetime
by John Baez 30 May '06

30 May '06

Dear Categorists: Some of you might like to see the transparencies of this talk: http://math.ucr.edu/home/baez/quantum_spacetime/ It's a general colloquium talk, where I'll try to explain to the physicists at the Perimeter Institute how higher categories show up in physics. You won't learn any category theory here. If you want details, there are links to some papers. Best, jb ............................................................................. Higher-dimensional algebra: a language for quantum spacetime Category theory is a general language for describing things and processes - called "objects" and "morphisms". In this language, the counterintuitive features of quantum theory turn out to be properties that the category of Hilbert spaces shares with the category of cobordisms - in which objects are choices of "space", and morphisms are choices of "spacetime". The striking similarities between these categories suggests that "n-categories with duals" are a promising framework for a quantum theory of spacetime. We sketch the historical development of these ideas from Feynman diagrams, to string theory, topological quantum field theory, spin networks and spin foams, and especially recent work on open-closed string theory, quantum gravity coupled to point particles, and 4d BF theory coupled to strings.

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HyLo 2006: Extended Deadline
by Carlos Areces 30 May '06

30 May '06

******************************************************************* HYLO 2006 DEADLINE EXTENDED! New deadline is Thursday June 1 ******************************************************************* FINAL CALL FOR PAPERS International Workshop on Hybrid Logic 2006 (HyLo 2006) Affiliated with LICS 2006 August 11, 2006, Seattle, USA ******************************************************************* AIMS AND SCOPE: Hybrid logic is a branch of modal logic in which it is possible to directly refer to worlds/times/states or whatever the elements of the (Kripke) model are meant to represent. Although they date back to the late 1960s, and have been sporadically investigated ever since, it is only in the 1990s that work on them really got into its stride. It is easy to justify interest in hybrid logic on applied grounds, because of the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant,and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem (the basic mechanism being to add nominals --- atomic symbols true at a unique point --- together with extra modalities to exploit them) often actually improves the behavior of the underlying modal formalism. For example, it becomes far simpler to formulate modal tableau, resolution, and natural deduction in hybrid logic, and completeness and interpolation results can be proved of a generality that is not available in orthodox modal logic. Hybrid logic is now a mature field, therefore a theme of special interest at this HyLo workshop will be the combination of hybrid logic with other logics, the basic methodological question being "what is the best way of hybridizing a given logic?" However, submissions in all areas of hybrid logic are welcome. The workshop HyLo 2006 is likely to be relevant to a wide range of people, including those interested in description logic, feature logic, applied modal logics, temporal logic, and labelled deduction. The workshop continues a series of previous workshops on hybrid logic, for example the LICS-affiliated HyLo 2002 (http://floc02.diku.dk/HYLO) which was held as part of FLoC 2002, Copenhagen, Denmark. If you are unsure whether your work is of relevance to the workshop, please do not hesitate to contact the workshop organizers for more information. Contact details are given below. For more general background on hybrid logic, and many of the key papers, see the Hybrid Logics homepage (http://hylo.loria.fr/) INVITED SPEAKERS: Patrick Blackburn (INRIA Lorraine, France) Title: Hybrid Logic and Temporal Semantics Valeria de Paiva (PARC, USA) Title: Constructive Hybrid Logics and Contexts Ian Horrocks (University of Manchester, UK) Title: Hybrid Logics and Ontology Languages PROGRAM COMMITTEE: Carlos Areces (INRIA Lorraine, France) Patrick Blackburn (INRIA Lorraine, France) Thomas Bolander (Technical University of Denmark) Torben Bra=FCner (Roskilde University, Denmark) --- Chair Valeria de Paiva (PARC, USA) Melvin Fitting (Lehman College, New York, USA) Balder ten Cate (University of Amsterdam, The Netherlands) J=F8rgen Villadsen (Roskilde University, Denmark) SUBMISSIONS: We invite the contribution of papers reporting new work from researchers interested in hybrid logic. The revised version of accepted papers will be published online in an Elsevier ENTCS (http://www.elsevier.com/locate/entcs/) volume devoted to FLoC 2006 satellite workshops. A preliminary version of the proceedings will also be distributed at the workshop. One author for each accepted paper must attend the workshop in order to present the paper. Please use the HyLo 2006 submission page (http://www.easychair.org/HyLo2006/) handled by the EasyChair conference system, to submit papers. Papers should not exceed 15 pages including references. Authors are strongly encouraged to prepare their submissions according to the ENTCS guidelines (http://www.entcs.org/) IMPORTANT DATES: Deadline for submissions: June 1, 2006 (strict) Notification of acceptance: June 20, 2006 Deadline for final versions: July 21, 2006 CONTACT DETAILS: See the workshop homepage (http://hylomol.ruc.dk/HyLo2006) for further information. Please send all correspondence regarding the workshop to the organizers: Patrick Blackburn http://www.loria.fr/~blackbur/ Thomas Bolander http://www.imm.dtu.dk/~tb/ Torben Bra=FCner --- Chair http://www.ruc.dk/~torben/ Valeria de Paiva http://www.cs.bham.ac.uk/~vdp/ J=F8rgen Villadsen http://www.ruc.dk/~jv/

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Notes from Glasgow PSSL
by Tom Leinster 30 May '06

30 May '06

Dear all, Notes from some of the talks at the recent PSSL, including Jon Woolf's three-part introduction to derived categories, are available: http://www.maths.gla.ac.uk/~tl/pssl/#intellectual Contents: Miles Gould, "Coherence for categorified algebraic theories" Panagis Karazeris, "Flatness of functors into sites" Jürgen Koslowski, "What is the correct notion of morphism for interpolative semigroups?" Tom Leinster, "A universal Banach space" Jon Woolf, "Derived categories 1, 2, 3" Best wishes, Tom -- Tom Leinster <tl(a)maths.gla.ac.uk>

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Joseph Goguen Festschrift -- Call for Participation
by Joseph Goguen Festschrift 29 May '06

29 May '06

Algebra, Meaning, and Computation: A Festschrift Symposium in Honor of Joseph Goguen THIRD CALL FOR PARTICIPATION !!!URGENT: HOTEL ROOMS MUST BE BOOKED SOON!!! Joseph Goguen is one of the most prominent computer scientists worldwide. His numerous research contributions span many topics and have changed the way we think about many concepts. Our views about data types, programming languages, software specification and verification, computational behavior, logics in computer science, semiotics, interface design, multimedia, and consciousness, to mention just some of the areas, have all been enriched in fundamental ways by his ideas. A Symposium to honor Joseph Goguen on his 65th birthday on June 28, 2006 will be held at the Computer Science and Engineering Department of the University of California in San Diego (UCSD) in June 27-29 2006. There will also be an IFIP WG1.3 meeting co-located with the Symposium that will take place on June 30. Leading researchers in the different areas spanned by Joseph Goguen's work have contributed over thirty papers to the Festschrift volume being published by Springer-Verlag. These papers will be presented at the Symposium in a three full day programme. A Symposium banquet is planned for June 28 to celebrate Joseph Goguen's 65th Birthday. The Symposium organizers welcome participation by any members of the scientific community who would like to take part in this important event. LOCAL INFORMATION AND VENUE The UCSD Campus is located in La Jolla, on top of a spectacular mesa overlooking the Pacific Ocean. The Symposium, and also the IFIP WG1.3 meeting, will be held at UCSD's Computer Science Department. The town of La Jolla is one of the most beautiful in the California Coast. Weather in June should be very pleasant, typically around 25 degrees Celsius, mostly sunny but possibly with some morning coastal fog. La Jolla is easy to reach from the San Diego Airport (see below). All major US airlines fly into San Diego from other main hubs like Los Angeles, San Francisco, Washington DC, New York, Chicago, Dallas, and so on. The Festschrift Symposium in Honor of Joseph Goguen is being hosted by the Jacobs School of Engineering's Department of Computer Science and Engineering. The meetings will be held in the Computer Science and Engineering Building's main Auditorium, room 1202. For a map of the campus and directions to UCSD CSE Department see http://formal.cs.uiuc.edu/goguenFest/ SYMPOSIUM HOTEL A block of rooms at a special reduced rate been reserved for this event at the Best Western La Jolla Inn by the Sea, which is conveniently located at the heart of downtown La Jolla and very close to the Ocean. -Website: http://lajollainnbythesea.com/ -Total is $139.00/night (approx. $153.59/night after tax) -Reservation Deadline: May 26th: all unbooked rooms will be released on May 26th -Parking fees at the hotel have been waived for our group How to make a reservation. Call: 800-462-9732 (from within the U.S.) 800-526-4545 (from within California and Canada) Email: innbyseabw(a)aol.com Mention confirmation #203732 or UCSD/Computer Science & Engineering (Note: a previous mistake about the hotel phones has been corrected) Transportation from the San Diego airport to the Best Western Hotel (Both terminals 1 & 2) is provided by Cloud 9 Shuttle for $16.00. This is the cheapest way to get to the hotel and the fee can be directly charged to the hotel room. The shuttle runs 24 hours a day. Taxi or rental car are alternative options. SYMPOSIUM REGISTRATION The early registration fee of $255.00 - gives access to the entire Festschrift event. This includes meetings on June 27 - 29, snacks and drinks during the meeting, lunches on all 3 days, Festschrift volume, Concert with Wine & Cheese Reception on June 27th, banquet on June 28th and transportation to and from hotel for events. The registration fee of $51.00 for the IFIP WG 1.3 Meeting on June 30th includes snacks & drinks during the meeting, lunch, and transportation to and from hotel. The registration can be made using a credit card at the symposium registration website: https://secure.ucsd.edu/external/cse-festschrift/ Early registration is strongly encouraged. A registration fee of $300 will be required after June 11, and a late registration fee of $350 after June 21st. BOOK SOON! Participants are strongly encouraged to register as soon as possible, and also to proceed immediately with booking of their hotel room and airline tickets. June is a high tourist season in La Jolla, and late booking of airline tickets, or of hotel rooms not under the special conditions mentioned above, can be difficult and significantly more expensive. SYMPOSIUM PROGRAM A preliminary version of the Symposium schedule can be found in http://formal.cs.uiuc.edu/goguenFest/ ORGANIZATION Program Committee Kokichi Futatsugi, JAIST, Japan Jean-Pierre Jouannaud, Ecole Polytechnique, France Jose Meseguer, University of Illinois at Urbana-Champaign, USA Local Chair Keith Marzullo, UCSD, USA Main Symposium Coordinator Ms. Briana Ronhaar Computer Science & Engineering University of California, San Diego 9500 Gilman Dr. #0404 La Jolla, CA 92093-0404 Email: bronhaar(a)cs.ucsd.edu Phone: ++1-858-822-5198 Fax: ++1-858-822-1559

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Bill Hatcher -- an obituary
by Peter Freyd 29 May '06

29 May '06

[Bill's category papers were concerned mostly with categories of algebras, his non-mathematical works with the spreading of the Baha'i faith.] The Globe and Mail 29 May 2006 LIVES LIVED Facts & Arguments William S. Hatcher Roshan Danesh 663 words A18 Husband, father, mathematician, philosopher, pursuer of authenticity. Born Sept. 20, 1935, in Charlotte, N.C. Died Nov. 27, 2005, in Stratford, Ont., of a heart attack, aged 70. I always looked up to my uncle, William Hatcher. Truly, almost everyone who met him looked up to him. At 6-foot-6, and with the physical size and booming voice that betrayed his roots in the deep south of the United States, he was pretty much always the largest presence wherever he found himself. But for my uncle Bill, physical presence was merely the reflection of the other ways in which he was a towering figure. His mind was what made him most well-known. He brought an iron-clad precision and clarity to the most ubiquitous, essential, and seemingly eternal questions of human life. In his early 20s, he began contemplating a logical proof of the existence of God. When he fully completed the proof some decades later, he travelled over many years to universities across Canada, the United States, and Europe, where he explicated the proof to packed audiences. The logical proof was one of Bill's most characteristic achievements. It was the perfect blending of the two passions of his mind science and religion. A mathematician and philosopher at Universiti Laval for more than 30 years, he was listed as one of the eight Platonist philosophers of the latter half of the 20th century in the respected Encylopidie Philosophique Universelle. His contribution to the study of religion, and in particular the Baha'i faith a subject on which he co-authored the seminal introductory text led him to be recognized as one of the greatest scholars of Baha'i studies. But it was uncle Bill's qualities of heart that I will remember most. He was staunchly committed to the pursuit of authentic relationships and the principle that love is expressed through self-sacrifice, service, altruism, and putting others ahead of oneself. He captured this theme in his book Love, Power, and Justice: The Dynamics of Authentic Morality. One time he said I should simply look around me when walking down the street and reflect on my reaction to those I saw. He was giving me a lesson about how to stay conscious of my own prejudices, my own self-interested commitments which, he insisted, were reflections of a failure to authentically love and relate to other human beings. Uncle Bill constantly pursued authenticity in his own life, and strived to live a life characterized by service to others. Of course, he sometimes failed, but he often succeeded. Sometimes his actions took the form of grand gestures such as moving to Russia at a dangerous time because there were contributions he could make as the society emerged from the communist era. Other times it was in the simple sweetness of how he always was prepared to listen to one's ideas, share his thoughts, and encourage one to do better. Like all high-achievers, Bill was constantly striving to do better. In the last few years, he seemed to become a little doubtful of whether his myriad accomplishments (raising three children with his wife Judith, training thousands of young minds, publishing more than 50 books and articles, being a leader of the Baha'i community of Canada and one of its leading scholars) were enough. To those of us who knew him intimately and loved him dearly, it was hard to take such insecurities seriously. My uncle Bill touched the hearts of thousands of people, and helped educate, refine, and inspire their minds. The gifts he gave others through his writings and teaching, and his acts of kindness, were more than we could fairly expect from anybody. The gift he gave me was clear: Be humble, strive as hard as you can, and be a lover of humanity. I will cherish that gift forever. Roshan is William Hatcher's nephew. Illustration

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jobs: 1 PhD and 1 Post-doc position at CWI, Amsterdam
by F.S.de.Boer＠cwi.nl 20 May '06

20 May '06

======================================================================= CWI: 1 PhD Position and 1 Postdoc Position in the CREDO Project ======================================================================= The theme SEN3 Coordination Languages at CWI (http://www.cwi.nl) has 1 PhD position for four years and 1 postdoc position for three years. Both positions are within the IST-33826 research CREDO project "Modeling and analysis of evolutionary structures for distributed services", recently funded by the European Union. This project starts September 1, 2006, and lasts for three years. The objective of this project is the development and application of an integrated suite of tools for compositional modelling, testing, and validation of software for evolving networks of dynamically reconfigurable components. More information on this project can be found at the following webpage: http://www.cwi.nl/projects/credo. Job description --------------- The candidates are expected to work on the design and development of a new high-level modelling language Credo for the dynamic composition of highly reconfigurable component-based software systems, and light-weight and automated verification techniques and tools supporting this language. The main overall idea of Credo is the integration of a formal component model based on concurrent objects which support run-time updates with a new model of component connectors based on mobile channels. The main objective of this integration is to support rapid prototyping and automated validation of networks of distributed services implemented by components, focusing on analyzing the effect of dynamic reconfiguration. The kernel of the Credo tool will consists of an abstract interpreter for the language implemented in the rewriting logic of the Maude system (http://maude.cs.uiuc.edu) The abstract interpreter forms the basis for the development and integration of simulation, testing and validation tools for the compositional analysis of functional, timing, and resource requirements. Bothe candidates should have a background in software engineering, concurrency and distributed systems, and practical software development or formal methods. The PhD candidate should have at least a master degree in computer science and the candidate for the postdoc position should have a PhD degree in computer science. Scientific Cluster of Software Engineering at CWI ------------------------------------------------- CWI is an internationally renowned research institute in mathematics and computer science, located in Amsterdam, The Netherlands. The theme SEN3 Coordination Languages of the Scientific Cluster of Software Engineering at CWI is a dynamic group of internationally recognized researchers who work on Coordination Models and Languages and Component-Based Software Composition. The activity in SEN3 is a productive, healthy mix of theoretical, foundational, and experimental work in Computer Science, ranging in a spectrum covering mathematical foundations of models of computation, formal methods and semantics, implementation of advanced research software systems, as well as their real-life applications. Terms of employment ------------------- The salary and terms at CWI are in accordance with the Dutch "CAO-onderzoeksinstellingen". The initial salary for a Ph.D. student is Euro 1848,- gross per month. The salary grows to Euro 2367,- in the fourth year. The salary is supplemented with a holiday bonus of 8% and an end-of-year bonus of 4.1 %. The initial salary for a postdoc is around Euro 2803,- (Euro 2848,- per 1/8/06) gross per month. The salary is supplemented with a holiday bonus of 8% and an end-of-year bonus of 4.1 %. CWI offers very attractive working conditions, including flexibility and help with housing for foreigners. Further details --------------- More information can be obtained Dr. F.S. D Boer, telephone +31-20-592-4139, email F.S.de.Boer 'at' cwi.nl. How to apply ------------ To apply, please send a statement of your interest, together with curriculum vitae, letters of references, and possibly list of publications to F.S.de.Boer 'at' cwi.nl. Make sure that you specifically mention the CREDO project.

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Hecke eigensheaves and KV 2-vectors
by Urs Schreiber 19 May '06

19 May '06

Dear category theorists, if you don't mind, I'd like to mention a naive observation. Attention of physicists, like myself, has recently been drawn to the geometric Langlands conjecture - since E. Witten and A. Kapustin have pointed out how it can be understood in terms of 2-dimensional topological field theory. Even after having been introduced to some basics, I hardly know anything about geometric Langlands. But I believe I do understand some aspects of 2D topological field theory. In particular, I am fond of the general fact that where \C-modules (\C = the complex numbers) appear in 1D quantum field theory (quantum mechanics), we see C-modules appear in 2D TFT, where now C is some abelian monoidal category. In the most accessible cases of topological field theory we have C = Vect. Now, the 2-category (bicategory) Vect-Mod contains that of Kapranov-Voevodsky 2-vector spaces, but is larger than that (isn't it?). In general, it should make some sense to address objects in C-Mod (module categories for C) as categorified vector spaces; and 1-morphisms in C-Mod as categorified linear maps between these. Interestingly, when one studies 2D quantum field theory (topological or conformal), one finds that boundary conditions of the theory (known as "D-branes") are described by objects of objects of C-Mod, i.e. objects of C-module categories. In the above terminology these would be like categorified vectors. Moreover, there are phenomena called "defect lines" or "disorder operators" in 2D QFT. These are known to be described by 1-morphisms in C-Mod, i.e. by categorified linear maps. Therefore a "defect line" may be applied to a "D-brane", much like a linear map may be applied to a vector. The above analogy naturally motivates to contemplate the case where the D-brane is an eigenvector under this action, i.e. where it is sent by the action of the defect line to itself, up to tensoring with an element in C. This might be nothing but a play with words. But, remarkably, Witten and Kapustin point out that the Hecke eigensheaves appearing in the context of geometric Langlands are precisely to be identified with certain D-branes that are categorified eigenvectors of some defect line, in the above sense. Of course, they do not say so using category theoretic terminology. They are addressing an audience of physicists. At one point they apologize for mentioning the term "functor" once. Therefore I was wondering what people knowledgeable in (higher) category theory would think of this. Does my observation make sense? (Of course I am glossing over a couple of technical details.) If yes, has it been observed before? Is it useful for anything? I'd be grateful for any kind of comments. Best regards, Urs Schreiber P.S. As before on previous occasions, I have written up some informal notes with slightly more details on what I have in mind here: http://golem.ph.utexas.edu/string/archives/000810.html

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