September 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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'Directed Algebraic Topology'
by Marco Grandis 29 Sep '09

29 Sep '09

Dear categorists, My book 'Directed Algebraic Topology' Models of non-reversible worlds has appeared, at Cambridge University Press. Its aims are mentioned below. It is likely well known that the policy of Cambridge UP, with respect to publication, is open and liberal. But I must say I was pleased and surprised, during the preparation of this volume, by their way of handling things, which was at the same time effective and informal, precise and very flexible. For the many people in this list that are concerned with the problems of our libraries, because of the high prices of scientific books and journals, I will add that royalties for this volume have been converted into CUP books for the library of my Departement. Marco Grandis ________ FROM THE BEGINNING OF THE INTRODUCTION Aims Directed Algebraic Topology is a recent subject which arose in the 1990's, on the one hand in abstract settings for homotopy theory, and on the other hand in investigations in the theory of concurrent processes. Its general aim should be stated as `modelling non-reversible phenomena'. The subject has a deep relationship with category theory. The domain of Directed Algebraic Topology should be distinguished from the domain of classical Algebraic Topology by the principle that {\it directed spaces have privileged directions and directed paths therein need not be reversible}. While the classical domain of Topology and Algebraic Topology is a reversible world, where a path in a space can always be travelled backwards, the study of non-reversible phenomena requires broader worlds, where a directed space can have non-reversible paths. The homotopical tools of Directed Algebraic Topology, corresponding in the classical case to ordinary homotopies, the fundamental group and fundamental $n$- groupoids, should be similarly `non-reversible': {\it directed homotopies}, the {\it fundamental monoid} and {\it fundamental $n$-categories}. Similarly, its homological theories will take values in `directed' algebraic structures, like {\it preordered} abelian groups or abelian {\it monoids}. Homotopy constructions like mapping cone, cone and suspension, occur here in a directed version; this gives rise to new `shapes', like (lower and upper) directed cones and directed spheres, whose elegance is strengthened by the fact that such constructions are determined by universal properties. Applications will deal with domains where privileged directions appear, such as concurrent processes, rewrite systems, traffic networks, space-time models, biological systems, etc. At the time of writing, the most developed ones are concerned with concurrency. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Congratulations to Steve
by Ross Street 29 Sep '09

29 Sep '09

Steve Lack has just been awarded the Australian Mathematical Society Medal for 2009: Australian Mathematical Society Medal recognises distinguished mathematical sciences research by members of the Australian Mathematical Society. Eligibility for the medal include the requirements that the Society member must be under the age of 40 years, and that a significant portion of the research was carried out in Australia. The Medal was first presented in 1981. It is awarded at the opening session of the Society's Annual Meeting. Congratulations Steve! Well deserved. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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2 new papers on higher category theory
by Mark.Weber＠pps.jussieu.fr 28 Sep '09

28 Sep '09

Greetings. The following 2 papers Algebras of higher operads as enriched categories II (joint with Michael Batanin and Denis-Charles Cisinski) http://arxiv1.library.cornell.edu/abs/0909.4715 Abstract: One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [2] to adapt the machinery of globular operads [1] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [4] of Gray categories. Moreover much of the previous work on the globular approach to higher category theory is simplified by our new foundations, and we illustrate this by giving an expedited account of many aspects of Cheng's analysis [3] of Trimble's definition of weak n-category. By way of application we obtain an ``Ekmann-Hilton'' result for braided monoidal 2-categories, and give the construction of a tensor product of A-infinity algebras. Free Products of Higher Operad Algebras http://arxiv1.library.cornell.edu/abs/0909.4722 Abstract: In this paper we continue the developments of [2] and [5] by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an n-operad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad. [1] M. Batanin. Monoidal globular categories as a natural environment for the theory of weak n-categories. Advances in Mathematics, 136:39103, 1998. [2] M. Batanin and M. Weber. Algebras of higher operads as enriched categories. Applied Categorical Structures, 38 pages, 2008. [3] E. Cheng. Comparing operadic theories of n-category, preprint, 2008. [4] S. Crans. A tensor product for Gray categories. Theory and applications of categories, 5:1269, 1999. [5] M. Batanin, D-C. Cisinski, and M. Weber. Algebras of higher operads as enriched categories II, preprint 57 pages, 2009. have recently been completed and are available at the above URL's or my new home-page http://sites.google.com/site/markwebersmaths/ Mark Weber [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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PSSL 89
by Marino Gran 26 Sep '09

26 Sep '09

PSSL 89 - Second announcement Dear Colleagues, The registration for attending the 89th Peripatetic Seminar on Sheaves and Logic, which will be held on the weekend of 12th-13th December 2009 in Louvain-la-Neuve, Belgium, is now open. The website of the conference can be found at the address http://homepages.vub.ac.be/~tvdlinde/pssl89.html In order to register you should complete the Registration Form here below, and e-mail it to any of the organisers before October 31st. Saturday's lunch and dinner, as well as Sunday's lunch will be offered to those PSSL participants who register by then. You can book your room directly: in order to benefit from the special prices for the PSSL participants, you should complete the "Fiche de Réservation" which may be downloaded from the PSSL website, and send this document to the address H2200-SB1(a)accor.com. Alternatively, you can ask any of the organisers to book the room for you. We are looking forward to seeing you in Louvain! Best regards, The organisers Enrico Vitale, Marino Gran, Tim Van der Linden, Tomas Everaert REGISTRATION FORM (please delete as appropriate) I, __________________________________________, would like to attend the 89th PSSL. My affiliation is _____________________________________ (University etc.). I intend to give a talk / I do not intend to give a talk. I would like to ask the organisers to book a single/double room at the Hotel Mercure for the nights of _____________ December. I would like to attend the dinner on Saturday / I would like to bring a guest / I will not be attending the dinner on Saturday. I have the following special dietary requirements: _________________________________________________________ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CMCS 2010 Pre-announcement/call for papers
by Alexandra Silva 25 Sep '09

25 Sep '09

[- apologies for multiple copies -] ------------------------------------------------------ CMCS 2010 Pre-announcement/call for papers ------------------------------------------------------ The Tenth International Workshop on Coalgebraic Methods in Computer Science 26-28 March 2010, Cyprus, Greece (co-located with ETAPS 2010) Webpage ----------- http://event.cwi.nl/cmcs10/ Contact ---------- cmcs10(a)cwi.nl Aims and scope ------------------ The aim of the workshop is to bring together researchers with a common interest in the theory of coalgebras and its applications. Over the last two decades, coalgebra has developed into a field of its own, presenting a mathematical foundation for various kinds of dynamical systems, infinite data structures, and logics. Coalgebra has an ever growing range of applications in and interactions with other fields such as reactive and interactive system theory, object oriented and concurrent programming, formal system specification, modal logic, dynamical systems, control systems, category theory, algebra, analysis, etc. An anniversary: the 10th CMCS ---------------------------------------- CMCS took place for the first time when ETAPS started, in 1998. Since then, it has always been collocated with ETAPS, becoming bi-annual since the start of CALCO (Conference on Algebra and Coalgebra) in 2005. In 2010, we will celebrate the 10th edition of CMCS, by inviting a number of specialists in the field to present overviews of both obtained results and future challenges. Programme Committee --------------------- ----- Chairs: Bart Jacobs (RUN) and Jan Rutten (CWI, VUA, RUN). Members: to be announced shortly. Organising Committee -------------------------- Bart Jacobs, Milad Niqui (co-chair, CWI), Jan Rutten, Alexandra Silva (co-chair, CWI). Submissions -------------- There are two types of submissions possible: (a) Papers to be evaluated by the PC for publication in the proceedings: They must have a length no greater than 20 pages. (Style files will be provided shortly.) They must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Accepted papers will appear in either ENTCS or EPTCS. Also a special journal issue of selected papers will be considered. (b) Short contributions: These will not be published in the proceedings but will be bundled in a CWI technical report. They should be no more than two pages and may describe work in progress, summarise work submitted to a conference or workshop elsewhere, or in some other way appeal to the CMCS audience. Important dates ------------------- * 8 January 2010: strict submission deadline regular papers * 13 February 2010: notification regular papers * 15 February 2010: deadline early registration * 20 February 2010: final version * 27 February 2010: strict submission deadline short contributions * 6 March 2010: notification short contributions * 26-28 March 2010: the workshop [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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infty-categories
by jim stasheff 25 Sep '09

25 Sep '09

Working witht the defintion and description of infty-category as in Lurie's What is a... in the Notices AMS with a weak/pseudo composition defined only up to homopy from filling a 2-horn I can see that 3-horns will give homotopy associativity what sort of coherence up to homotopy do the k-horns for k > 3 imply? reference? thanks jim [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Comma categories
by Tony Meman 25 Sep '09

25 Sep '09

Dear category theorists, I have two questions concerning comma categories. If C is a category with a terminal object *, is the comma category (C,*) consisting of arrows from C to * isomorphic to the category C itself? If this is true, the same should apply to the dual case with an initial object. The category sSet of simplicial sets is the category of functors from the opposite delta category Delta^op to Set. The category of pointed simplicial sets sSet* is defined as the comma category (delta0, sSet), where delta0=hom(-,[0]). Is sSet* isomorphic to the category of functors from ([0],Delta)^op to Set? Thank you in advance for any help. Tony [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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