January 2009 - Categories - categories.org.au

In answer to Paul Taylor
by Andree Ehresmann 22 Jan '09

22 Jan '09

In answer to Paul Taylor Charles Ehresmann has realized as soon as 1951 (cf. "Charles Ehresmann: Oeuvres complètes et commentées", Part I, p. 153) that in a pseudogroup of transformations only the open sets of the associated topology are used, not the points, whence the idea of replacing the pseudogroup of transformations by a groupoid and the topology by a paratopology (i.e., a complete distributive lattice). He formalized this idea in later works, in particular in the 1957 seminal paper "Gattungen von lokalen Strukturen" [Oeuvres, Part II, p. 126], where he replaces the pseudogroup of transformations by a local groupoid, and even, more generally, by a local category, that is a category equipped with a "local" order compatible with its structure (in modern term it is a category internal to a category of locales); and he develops the theory of complete local species of structures over a local groupoid, which generalizes that of a sheaf. Andrée

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Oxford position
by Ulrike Tillmann 22 Jan '09

22 Jan '09

We are about to advertise the position described below. A University Lectureship is the standard position at Oxford and should be comparable roughly with an Assistant or Associate Professorship in North American universities. I would be happy to receive any informal inquiries. Please note the deadline of 20 February. Ulrike Tillmann %%%%%%%%%%% Ad %%%%%%%%%% UNIVERSITY OF OXFORD Mathematical, Physical and Life Sciences Division Mathematical Institute in association with Keble College University Lecturership in Pure Mathematics The Mathematical Institute proposes to appoint a University Lecturer in Pure Mathematics with effect from 1 October 2009. The successful candidate will be appointed to a Fellowship at Keble College under arrangements described in the further particulars. The combined University and College salary will be on a scale up to £56,917 per annum. The successful candidate must have a record of outstanding research in some branch of pure mathematics. Preference will be given to applicants whose research interests are close to algebraic topology, broadly interpreted. Further particulars, containing details of the application procedure and of the duties, may be obtained from the Administrative Assistant (Vacancies), The Mathematical Institute, 24-9 St Giles' Street, Oxford OX1 3LB (vacancies(a)maths.ox.ac.uk) or by visiting http://www.maths.ox.ac.uk/notices/vacancies/ The closing date for applications is 20 February 2009. Please quote reference number BK/09/006. The University is an Equal Opportunities Employer.

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Foundations for Computable Topology
by Paul Taylor 21 Jan '09

21 Jan '09

Foundations for Computable Topology www.PaulTaylor.EU/ASD/foufct/ This paper is an overview of the whole of the Abstract Stone Duality research programme. I was invited to write it for a volume on Foundations of Mathematics that is more inclined towards philosophy than technicalities and has contributions from categorists, set theorists and philosophers. I advertised this in July, but the production timescale of this book has slipped somewhat, so I would still welcome comments. In particular, I have some questions below about citations for the history of category theory. The plan of the paper is as follows: 1. Foundations should be designed FOR mathematics. 2. The formal link between category theory and symbolic logic. 3. Using this as a methodology to design the new theory. 4. Stone duality between topology and algebra over sets 5. Stone duality as a monad, with applications to topology 6. The axiomatic "monadic framework". 7. The subobject classifier and Sierpinski space. 8. Axiomatic development of set theory using the Euclidean principle and topology using the Phoa principle. 9. Discrete mathematics using overt discrete spaces, arithmetic universes, recursion, description. 10. The "underlying set" axiom, which makes the full subcategory of overt discrete spaces into a topos. 11. Scott continuity as an axiom. 12. Beyond local compactness. The version of the last section as it appeared in July was COMPLETELY SCRAPPED, and replaced with a discussion of "equideductive logic", about which I talked at meetings in Sussex in September and Padova in October. Even in the present version, I still intend to replace the last few pages with a "conclusion". Briefly, equideductive logic is the (surprisingly interesting) logic of regular monos in a CCC with all finite limits. It is exactly what is required to perform Dana Scott's "equilogical space" construction, but without using the set theoretic interpretation based on the set of points of the basic spaces. I have done further work on this, but I am nowhere near being ready to advertise it. This paper does not discuss computation, but Andrej Bauer did some interesting programming during the summer: math.andrej.com/2008/08/24/efficient-computation-with-dedekind-reals/ SOME HOSTORICAL QUESTIONS Recall that the purpose of my paper is to give a general overview of the philosophy and motivations of ASD, along with a statement of all of the axioms for reference. I am therefore looking for citations that are also of a survey, historical or philosophical flavour, rather than the original technical source. The numbers refer to the subsections or paragraphs -- the paper is written in a narrative style, without Definition--Lemma--Theorem--Proof. The non-bracketed text is quoted from my paper. 2.6 [In a discussion of the relationship between category theory and symbolic logic.] Systems such as linear logic that do not obey all of the structural rules correspond to different categorical structures. These might, for example, be \emph{tensor} products~($\otimes$), which categorists understood long before they did predicate logic. 3.7 [In a critique of point--set topology.] Sheaves in algebraic geometry were based on open sets and not points 3.8 These books [on point--set topology] ... make little attempt to explore the full extent of even the world that is measured out by their own co-ordinate system. This was only begun when the analogy with the $\exists\land$-fragment of logic was recognised. 5.1 For this, we need a way of formulating (potentially infinitary) algebraic theories that works over an arbitrary category $\S$, and not just over the category of sets. Such an account is provided by the categorical notion of \emph{monad}. [Has anyone ever tried to write a textbook that covers the material of Modern or Universal Algebra using monads?] 6.12 The problem of finding splittings is actually not a new one: it was well known in homological algebra, which provided Jon Beck's original inspiration. [Can you give me a simple example of the use of splittings in homological algebra, and the difficulty in finding them?] 9.1 Finite limits and stable effective quotients of equivalence relations were studied in category theory long before it considered logic, because categories of finitary algebras inherit them from sets. 9.12 For terms and parameters of these types, Scott continuity is a \emph{theorem}, essentially the one of Henry Rice and Norman Shapiro. Paul Taylor pt09 @ PaulTaylor.EU www.PaulTaylor.EU/ASD/foufct

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Carnegie Mellon Summer School in Logic and Formal Epistemology
by Steve Awodey 20 Jan '09

20 Jan '09

Carnegie Mellon Summer School in Logic and Formal Epistemology In the summer of 2009, the Department of Philosophy at Carnegie Mellon University will hold a three-week summer school in logic and formal epistemology for promising undergraduates in philosophy, mathematics, computer science, linguistics, and other sciences. The goals are to o introduce students to cross-disciplinary fields of research at an early stage in their career; and o forge lasting links between the various disciplines. The summer school will be held from Monday, June 8 to Friday, June 26, 2009. There will be morning and afternoon lectures and daily problem sessions, as well as planned outings and social events. The summer school is free. That is, we will provide o full tuition, and o dormitory accommodations on the Carnegie Mellon campus. So students need only pay round trip travel to Pittsburgh and living expenses while there. There are no grades, and the courses do not provide formal course credit. Instructions for applying can be found on the summer school web page, http://www.phil.cmu.edu/summerschool Materials must be received by the Philosophy Department by March 15, 2009. This year's topics are: Categories and Structures Monday, June 8 to Friday, June 12 Instructor: Steve Awodey Decisions and Games Monday, June 15 to Friday, June 19 Instructor: Teddy Seidenfeld Logic and Formal Verification Monday, June 22 to Friday, June 26 Instructor: Jeremy Avigad The summer school is open to undergraduates, as well as to students who will be completing their first year of graduate school. Applicants need not be US citizens. There is a $20 nonrefundable application fee. Inquiries may be directed to Jeremy Avigad (avigad(a)cmu.edu)

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PSSL 88: new talk deadline
by Eugenia Cheng 19 Jan '09

19 Jan '09

PSSL 88 - supplementary announcement Dear all, We are delighted by the large number of registrations and talk proposals we have had for the PSSL in honour of the joint 60th birthdays of Martin Hyland and Peter Johnstone. However, we have already had more talks proposed than we can accommodate. Therefore if you would like to propose a talk and have not already done so, we now ask you to let us know by January 31st rather than the end of February as originally planned. The deadline for applying for funding is also January 31st, as before. The PSSL announcement email and registration form can be found here: http://cheng.staff.shef.ac.uk/pssl88/announce2.html Apologies for the inconvenience. Eugenia Cheng --- e.cheng(a)sheffield.ac.uk PSSL home page http://cheng.staff.shef.ac.uk/pssl88/

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Bangor mathematics web pages
by mail.btinternet.com 17 Jan '09

17 Jan '09

These have now transferred to http://www.math.bangor.ac.uk/ Please update your links. Ronnie Brown Previously this was http://www.informatics.bangor.ac.uk/public/mathematics

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Paper available: "A Lax-Algebraic Approach to Domain-Theoretic Topology"
by Rory Lucyshyn-Wright 16 Jan '09

16 Jan '09

My paper "A Lax-Algebraic Approach to Domain-Theoretic Topology" is available on my web site, at "http://www.math.yorku.ca/~rorylw/". The paper documents and builds upon results presented in my talk at the 2008 OctoberFest in Montreal. Your comments are welcome. Regards, Rory Lucyshyn-Wright

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Special volumes in honour of Francis Borceux and of Dominique Bourn
by Marino Gran 13 Jan '09

13 Jan '09

============================================== SPECIAL VOLUMES IN HONOUR OF FRANCIS BORCEUX AND OF DOMINIQUE BOURN ON THE OCCASION OF THEIR SIXTIETH BIRTHDAY Last year Francis Borceux and Dominique Bourn celebrated their 60th birthday, and an international meeting in their honour took place at the Royal Academy in Brussels last October (see http://www.math.ua.ac.be/bbdays/) We are glad to announce that there will be a Special Volume of the Cahiers de Topologie et Géométrie Différentielle Catégoriques dedicated to Francis Borceux, and a Special Volume of Theory and Applications of Categories dedicated to Dominique Bourn. Submission of papers on areas in which Francis Borceux and Dominique Bourn have worked are particularly encouraged. The deadline for submission for both volumes is 31 May 2009. Please find the instructions for submission of papers below. With our best wishes for the New Year, Jiri Adamek, Andrée Ehresmann, Marino Gran, George Janelidze, Rudger Kieboom, Jiri Rosicky, Walter Tholen and Enrico Vitale ================================================= - SPECIAL VOLUME FOR FRANCIS BORCEUX (CAHIERS): Please email your submission to Marino Gran (marino.gran(a)uclouvain.be) as an attached PDF file: you may suggest one of the Guest Editors Jiri Adamek Andrée Ehresmann Marino Gran George Janelidze Rudger Kieboom for this Special Volume to be assigned to your paper. Please be sure that you receive an e-mail acknowledging the receipt of your submission. All papers will be carefully refereed following the standards of Cahiers de Topologie et Géométrie Différentielle Catégoriques. ================================================ - SPECIAL VOLUME FOR DOMINIQUE BOURN (TAC): Please email your submission to Enrico Vitale (enrico.vitale(a)uclouvain.be) as an attached PDF file: you may suggest one of the Guest Editors Andrée Ehresmann George Janelidze Jiri Rosicky Walter Tholen Enrico Vitale for this Special Volume to be assigned to your paper. Please be sure that you receive an e-mail acknowledging the receipt of your submission. All papers will be carefully refereed following the standards of Theory and Applications of Categories.

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MFPS Deadlines Revised and Extended!
by MFPS 13 Jan '09

13 Jan '09

Dear Colleagues, The deadlines for submissions to MFPS 25 have been revised and extended. The new deadlines are: - January 20 Title and Short Abstract submission deadline - January 24 Paper submission deadline The other dates remain the same. Details about submission requirements and information about the meeting can be found at the MFPS 25 Home page http://www.math.tulane.edu/~mfps/mfps25.htm Submissions can be made to EasyChair by pointing your browser at http://www.easychair.org/conferences/?c=.120373;conf=mfps25 Mathematical Foundations of Programming Semantics http://www.math.tulane.edu/~mfps

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Paper available
by Walter Tholen 10 Jan '09

10 Jan '09

The paper "On the categorical meaning of Hausdorff and Gromov distances, I" by Andrei Akhvlediani, Maria Manuel Clementino and myself is available at http://arxiv.org/abs/0901.0618 and on my homepage at http://math.yorku.ca/~tholen/ The paper expands on ideas offered in Maria Manuel Clementino's talk at CT08 and in my talks at the Octoberfest in Montreal and at the Borceux-Bourn Birthday Conference in Brussels in October. We welcome comments. Regards, Walter Tholen.

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