July 2009 - Categories - categories.org.au

Research positions
by Maria Manuel Clementino 26 Feb '14

26 Feb '14

5-YEAR RESEARCH POSITIONS The Centre for Mathematics of the University of Coimbra (CMUC) invites applications for five 5-year research positions in all areas of Mathematics. Applicants should have a PhD in Mathematics and at least three years of post-doctoral experience, with an international-level publication record and demonstrated ability to perform independent research. Preference will be given to candidates working in one of the areas in which the members of CMUC are currently active. A very good command of English is required. The appointments will be made for three years, renewable for two more. Successful applicants are expected to develop research within the areas of interest of CMUC. They should also contribute to graduate studies, supervising students from the Department of Mathematics. The basic salary is equivalent to the index 195 of the Portuguese research career (in the order of 42 500 euros a year), in accordance with the Ciência 2008 guidelines http://alfa.fct.mctes.pt/apoios/contratacaodoutorados/edital2008 Benefits include private health insurance and social security. Applicants should send • cover sheet (available from www.mat.uc.pt/cmuc/coversheet.pdf) including names and contact information of three persons who can provide a letter of recommendation • curriculum vitae (publication list included) • a 5-year research proposal (2 pages max), emphasizing their own research goals as pdf files to cmuc(a)mat.uc.pt. The subject of the e-mail message must include the job reference C2008 FCTUC CMUC v15-v19. The deadline for applications is *September 10, 2008.* ------------------------------ More information can be found at www.mat.uc.pt

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separable locale
by Thomas Streicher 17 May '13

17 May '13

Recently rereading Fourman's "Continuous Truth" I came across the term "separable locale" but could nowhere find an explanation. Does it mean a cHa A for which there exists a countable subset B such that ever a in A is the supremum of those b in B with b leq a. This would be the point free account of "second countable", i.e. having a countable basis. Of course, second countable T_) spaces are separable, i.e. have a countable dense set. Is this reading the "usual" one? Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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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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FLoC 2010: Call For Workshops Deadline Extension
by Hitoshi Ohsaki 31 Jul '09

31 Jul '09

FLoC 2010: Call For Workshops Deadline Extension: Workshop proposals can now be submitted up to Sept. 1, 2009. The original Call for Workshops is at http://www.floc-conference.org/cfw.html . Organizers will be notified by October 15, 2009. Proposals should be submitted electronically to EasyChair at the following address: http://www.easychair.org/conferences/?conf=floc10cfw (Clearly indicate at the top of the proposal the relevant conference) For further enquiries or information, please contact: Philip Scott (FLoC Workshop Chair) Department of Mathematics and Statistics University of Ottawa Ottawa, Ont. Canada K1N 6N5 email: phil(a)site.uottawa.ca [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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preprint: Categories without structures
by Andre.Rodin＠ens.fr 30 Jul '09

30 Jul '09

Dear all, I would like to announce this recent preprint of mine: http://arxiv.org/abs/0907.5143 Title: Categories without structures Abstract: The popular view according to which Category theory provides a = support for Mathematical Structuralism is erroneous. Category-theoretic foundatio= ns of mathematics require a different philosophy of mathematics. While structur= al mathematics studies "invariant forms" (Awodey) categorical mathematics st= udies covariant transformations which, generally, don't have any invariants. In= this paper I develop a non-structuralist interpretation of categorical mathema= tics and show its consequences for history of mathematics and mathematics educ= ation. Andrei [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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(Pre)prints
by Michael Barr 29 Jul '09

29 Jul '09

I would like to call your attention to three relatively new items on my ftp site, all joint with John Kennison and Bob Raphael: Local extension of maps, Isbell duality, Isbell duality for modules. To see them, simply browse to ftp.math.mcgill.ca/pub/barr/pdffiles and click on Index.html. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Paper available: Clone Theory and Algebraic Logic
by Zhaohua Luo 29 Jul '09

29 Jul '09

The paper "Clone Theory and Algebraic Logic" is available at http://www.algebraic.net/ctal The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and right algebras over a clone are covariant and contravariant functors from the category to that of sets respectively. In this paper we show that first-order logic can be studied effectively using the notions of right and left algebras over a clone. It is easy to translate the classical treatment of logic into our setting and prove all the fundamental theorems of first-order theory algebraically. Zhaohua Luo [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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2 new presentations
by RONALD BROWN 29 Jul '09

29 Jul '09

I have made pdf files of two recent presentations available from www.bangor.ac.uk/r.brown/askloster.html Some intuitions of higher dimensional algebra, and potential applications Category theory, higher dimensional algebra, groupoid atlases: prospective descriptive tools in theoretical neuroscience Ronnie [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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FICS'09 Call for participation - Fixed Points in Computer Science (CSL'09 workshop)
by Tarmo Uustalu 28 Jul '09

28 Jul '09

Call for Participation 6th Workshop on Fixed Points in Computer Science, FICS 2009 Coimbra, Portugal, 12-13 September 2009, a satellite workshop of CSL 2009, colocated with PPDP 2009, LOPSTR 2009 http://cs.ioc.ee/fics09/ Background Fixed points play a fundamental role in several areas of computer science and logic by justifying induction and recursive definitions. The construction and properties of fixed points have been investigated in many different frameworks such as: design and implementation of programming languages, program logics, databases. The aim of the workshop is to provide a forum for researchers to present their results to those members of the computer science and logic communities who study or apply the theory of fixed points. Previous workshops where held in Brno (1998, MFCS/CSL workshop), Paris (2000, LC workshop), Florence (2001, PLI workshop), Copenhagen (2002, LICS (FLoC) workshop), Warsaw (2003, ETAPS workshop). Topics for the call for papers included, but were not restricted to: * categorical, metric and ordered fixed point models * fixed points in algebra and coalgebra * fixed points in languages and automata * fixed points in programming language semantics * the mu-calculus and fixed points in modal logic * fixed points in process algebras and process calculi * fixed points in the lambda-calculus, functional programming and type theory * fixed points in relation to dataflow and circuits * fixed points in logic programming and theorem proving * finite model theory, descriptive complexity theory, fixed points in databases Invited speakers Robin Cockett (University of Calgary) Javier Esparza (Technische Universität München) Yde Venema (Universiteit van Amsterdam) Contributed talks Loredana Afanasiev and Balder ten Cate On core XPath with inflationary fixed points Lars Birkedal, Kristian Støvring and Jacob Thamsborg Solutions of generalized recursive metric-space equations Pierre Clairambault Least and greatest fixpoints in game semantics Zoltán Ésik and Stephen L. Bloom Scattered algebraic linear orderings Stephan Kreutzer and Martin Lange A note on the relation between inflationary fixpoints and least fixpoints of higher order Omer Landry Nguena Timo and Pierre-Alain Reynier On characteristic formulae for event-recording automata Robert Myers Regular expressions and the coalgebraic mu-calculus Milad Niqui and Jan Rutten Coinductive predicates as final coalgebras Pawel Parys Lower bound for evaluation of mu-nu fixpoint Dulma Rodriguez and Martin Hofmann Membership checking in greatest fixpoints revisited Daniel Stamate A bilattice based fixed point semantics for integrating imperfect information Kohtaro Tadaki Fixed points on partial randomness Yoshinori Tanabe and Masami Hagiya Fixed-point computations over functions on integers with operations min, max and plus Balder ten Cate and Gaelle Fontaine An easy completeness proof for the modal mu-calculus on finite trees Lionel Vaux A non-uniform finitary relational semantics of system T Programme committee Yves Bertot (INRIA Sophia Antipolis) Anuj Dawar (University of Cambridge) Peter Dybjer (Chalmers University of Technology) Zoltán Ésik (University of Szeged) Masahito Hasegawa (Kyoto University) Anna Ingólfsdóttir (Reykjavik University) Ralph Matthes (IRIT, Toulouse) (co-chair) Jan Rutten (CWI and Vrije Universiteit Amsterdam) Luigi Santocanale (LIF, Marseille) Alex Simpson (University of Edinburgh) Tarmo Uustalu (Institute of Cybernetics, Tallinn) (co-chair) Igor Walukiewicz (LaBRI, Bordeaux) Registration and cost Registration is through the CSL/PPDP/LOPSTR website. The FICS participation fee of 80 EUR includes 4 coffee breaks and the workshop dinner on Saturday. All workshop participants will receive a copy of the informal workshop proceedings. The early registration deadline for the CSL/PPDP/LOPSTR main conferences is 31 July. For FICS, there is no early/late rate difference. Sponsors EXCS, Estonian Centre of Excellence in Computer Science [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Sheaf toposes and chain-complete posets
by Andrej Bauer 28 Jul '09

28 Jul '09

Dear categorists, I am trying to wrap my mind around the concept of an (internal) chain-complete poset in a sheaf topos. I am failing to come up with an example of a poset that is chain-complete but is not complete. The precise definitions of "chain-complete" in the internal language are as follows. Suppose (P, <=) is a poset in a topos. For C in Omega^P, let chain(C) be the statement forall x, y : P, (x in C and y in C) ==> (x <= y or y <= x) Then P is chain-complete if forall C : Omega^P, chain(C) ==> exists x : P, x is the supremum of C where "x is the supremum of C" means the usual thing. So what does a chain-complete poset which isn't complete look like? Since I am used to arguing intuitionistically, it would help a lot if there were some (possibly infinitary) logical principle or schema that is typical of sheaf toposes -- something expressing the local nature of validity. Such a principle ought to be invalid in realizability toposes, so perhaps it should express or imply cocompleteness (with respect to Set). But would that be of any help for arguing in the internal language? With kind regards, Andrej Bauer [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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