September 2008 - 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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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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mathematical objects
by Charles Wells 01 Oct '08

01 Oct '08

Readers of this list may be interested in my new blog post, Mathematical objects in Wikipedia<http://gyregimble.blogspot.com/2008/09/mathematical-objects-in-wikipedia.ht…> . -- Charles Wells professional website: http://www.cwru.edu/artsci/math/wells/home.html blog: http://www.gyregimble.blogspot.com/ abstract math website: http://www.abstractmath.org/MM//MMIntro.htm personal website: http://www.abstractmath.org/Personal/index.html

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Group and abelian group objects in the category of Kelley spaces
by Bill Rowan 30 Sep '08

30 Sep '08

Hi all, Does anyone know of a good place where someone has written down the basic properties of such objects? As an example, if we have an (abelian, say) topological group, there is a natural uniform topology on the group such that the operations are uniformly continuous. Does the same hold for abelian group objects in the category of Kelley spaces? But anything would be helpful. Bill Rowan

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George Janelidze
by jim stasheff 29 Sep '08

29 Sep '08

Contact has been established - thanks to all those many who helped jim

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Subtoposes of Eff
by Prof. Peter Johnstone 29 Sep '08

29 Sep '08

Readers of Jaap van Oosten's new book on realizability will have come across the statement on p. 235 that the question "Is Set the only Grothendieck topos which occurs as a subtopos of the effective topos?", which Ieke Moerdijk asked him at his Ph.D. viva in 1991, is still unanswered. In fact I've known the answer to this question for at least five years: I referred to it in my talks at the European category theory meeting in Haute-Bodeux (September 2003) and the meeting on Ramifications of Category Theory in Firenze (November 2003). However, the proof hasn't been published anywhere (it will of course be in volume 3 of the Elephant when that is published -- and please don't ask me to predict when that will be!), so I thought I should let people know about it. We work in the realizability topos over an arbitrary pca A (all unexplained notation can be found in Jaap's book). Andy Pitts showed in his thesis that local operators on this topos correspond to maps j: PA --> PA whch "are nuclei in the logic of A-realizability", and that the corresponding subtopos of sheaves is equivalent to Set (or degenerate) iff the intersection \bigcap_{a \in A} j({a}) is inhabited. Suppose this condition fails; we shall show that the subtopos of j-sheaves is not complete. Let A_1 denote the assembly with underlying set A and [[a \in A_1]] = {a} for all a, and A_2 the assembly with the same underlying set and [[a \in A_2]] = j({a}). Note that A_2 is the j-closure of A_1 in \nabla A, and hence its associated j-sheaf. Also, by the assumption we've made, it is not the whole of \nabla A. We claim that the product of A copies of A_2 cannot exist in the topos of sheaves: if it did, it would obviously be a subobject of \nabla(A^A) (the latter being the product of A copies of \nabla A) and hence an assembly; moreover, its underlying set would be the whole of A^A since the forgetful functor from assemblies to Set (is representable, and hence) preserves all products which exist. Writing P for the product, for each a \in A the a^th projection A^A --> A must be trackable as a morphism P --> A_2; let e_a be an element of A which tracks it. Since A_2 is not the whole of \nabla A, we can find f(a) such that e_aa \not \in [[f(a) \in A_2]] (if e_aa is undefined, choose f(a) to be any element of A). Then f: A --> A has no realizers as a member of P. Peter Johnstone

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Re: BourWiki-iBourbaki-FunctorWiki?
by Andre Joyal 29 Sep '08

29 Sep '08

Dear Ellis Cooper, >Since this project entails substantial programming effort, I would >like to measure the >level of support the project could expect from the category-oriented >research community. >Your judgement is much appreciated. In addition to the peoples who have expressed their support in public many have done it privately. None have opposed it yet. Some peoples have expressed doubts about the feasability. In a letter to some of my correspondants I wrote: >The iBourbaki project is by nature a very long term project. >Mathematics is vast, and it may take a few generations to fully integrate >the main body of mathematics to iBourbaki. >Also the potential contributors will refuse to work seriously >on something that may disappear a few years later. >They should have the possibility of making lasting contributions. >Hence we should make sure that iBourbaki can last for more than one generation. >It will be like building a cathedral! >Of course, iBourbaki should evolve, since mathematics and the technology evolve. >But mathematics is also remarquably stable. >The mathematics of Euclid is still valid today, inspite of the >fact that we now have non-euclidian geometry. >I expect that the main corpus of iBourbaki will not change very much over long period of times. >We need to conciliate long term duration with the rapid developpement of technology. The realisation of iBourbaki depends on the collaboration of the mathematical community in large, not only of category theorists. It also depends on the collaboration and support of a group of computer scientists. My task at this point is to convince peoples that the project is worthy and feasable. André -------- Message d'origine-------- De: Ellis D. Cooper [mailto:xtalv1@netropolis.net] Date: mar. 23/09/2008 09:33 À: Joyal, André; categories(a)mta.ca Objet : categories: BourWiki-iBourbaki-FunctorWiki Dear Andre Joyal and categorists, Various networking models for collaborating on mathematics have been alluded to or suggested on this list (which is itself based on the listserv networking model). ********************************************************************************************************* Patrik Eklund on 7 Oct 2007 wrote: "Sound-video" is nothing but Skype, but adding whiteboards, that can be saved and worked with also offline, you have very good possibilities. The whiteboard mainly accepts non-formatted text, drawings and images. You can read doc and ppt file which are "pasted" as bitmaps on the whiteboard. They include desktop sharing if that would be required. Mathematical text I add through LaTeX, compiling, converting to pdf, and using the snapshot tool to paste bitmapped formulas on the whiteboard. ********************************************************************************************************* Dusko Pavlovic on 15 Sep 2008 wrote: an improved process, combining the integrity, and perhaps the structure of the categories@mta community with the available wiki-methods may bring categorical methods into a dynamic environment, perhaps more natural for them than books and papers. ********************************************************************************************************* Andrej Bauer on 16 Sep 2008 wrote: the usual kind of wiki is not suitable for collaborative science, but recently there has been news of a special wiki for scientists which has good support for references, keeps track of who said what, and has a rating system. ********************************************************************************************************* Meredith Gregory on 21 Sep 2008 wrote: - What is missing in most mathematical presentations is a view into the often very human and very messy process of getting to the presentation. <snip> Ever since Andre Joyal mentioned a 2nd life for Bourbaki i can't stop thinking about a Bourbaki colloquium run in Second Life <http://secondlife.com/> ********************************************************************************************************* Jacques Carette on 22 Sep 2008 wrote: I hereby volunteer my time and the technical resources I have at my disposal to 'host' a "New Bourbaki based on CT" project. ********************************************************************************************************* John Baez on 22 Sep 2008 wrote: Mathematics may be too much in a state of foundational flux for a systematic approach to be successful right now. Maybe the best we can hope for is something a bit more like Wikipedia, where different people contribute different portions of text, and they don't cohere in a polished whole. But presumably anyone calling for a new Bourbaki wants something different from Wikipedia. <snip> I would like to see lots of people try lots of different things. ********************************************************************************************************* A network model not yet mentioned is the multiple-thread technical support forum. See, for example http://www.theimagingsourceforums.com/forumdisplay.php?f=6 http://www.essentialobjects.com/Forum/Default.aspx http://www.codeproject.com/KB/ajax/ http://www.codeproject.com/Lounge.aspx?msg=2730104#xx2730104xx Technical support forums centralize expertise, whereas collaborative mathematics would best have mutually supportive distributed expertise. Each thread would be moderated to maintain topic and civility, like the categories listserv. Crucial to much mathematical collaboration is sharing of diagrams alongside mathematical expressions and natural language text. A webcam over a pad provides this important function. I myself have used Skype to discuss one-sided limits with my son who is away at college, where instead of looking at each other's face we aimed our webcams at pads. One step beyond separate pads beneath webcams is the idea of a "virtual drawing" which per discussion thread would overlay appropriately transparent images from multiple collaborators: a shared blackboard in your web browser. A web-site for collaborative mathematics could combine the secure multiple-thread forum model with virtual drawing. Every participant would have the option to record part or all of a thread for off-line review. Combined with video-conferencing via Skype or the like, real-time collaboration is an option. Since this project entails substantial programming effort, I would like to measure the level of support the project could expect from the category-oriented research community. Your judgement is much appreciated. Ellis D. Cooper

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Octoberfest - Proposed schedule of talks
by Robert Seely 27 Sep '08

27 Sep '08

We have a proposed schedule of talks for the Octoberfest meeting next weekend (4-5 Oct). Please be aware that changes may still happen, and a final schedule will be given out at the meeting itself. An html version of this document is available at the meeting website, and you can check there for any last-minute changes, as we know them. http://www.math.mcgill.ca/triples/octoberfest08.html Some talks are still "TBA" - I hope the speakers will give me titles asap! We have some abstracts - those we have will be available on the webpage (and I'll put others there as I get them). In addition, I suggest folks review the instructions on the website re location of the talks (at Concordia's Faubourg building), parking in the area (the university has indoor parking from 9am - a bit of a tight squeeze in terms of time, but possible - and there is metered parking on the streets around the area), and do check the weather (there are links to two weather sites on the webpage). -= rags =- ----------- Octoberfest08 Category Theory Octoberfest Concordia University, Montreal Saturday - Sunday, October 4 - 5, 2008 Proposed Schedule of Talks Room FGB040 (Faubourg building) Saturday, 4 October - morning session 9:15-9:45 M Makkai Revisiting the coherence theory for bicategories and tricategories 9:45-10:15 V Harnik TBA coffee break 10:45-11:15 W Tholen Towards an enriched understanding of Hausdorff and Gromov metrics 11:15-11:45 C Hermida TBA 11:45-12:15 M Warren Types and groupoids lunch afternoon session, in honour of P.J. Scott 2:00-2:30 P Hofstra From poset to quantifier 2:30-3:00 R Cockett Differentiation, linear matters, and other discussions from the Green Door 3:00-3:30 J Lambek In praise of quaternions coffee break 4:00-4:30 B Redmond Safe recursion revisited 4:40-4:50 J Morton 2-Vector Spaces and Finite Groupoids 4:50-5:10 T Kusalik The Continuum Hypothesis in topos theory and algebraic set theory 5:10-5:30 R Lucyshyn-Wright TBA 5:30-6:00 G Lukacs TBA 6:00-6:20 C Nourani Functorial parallel worlds model computations free evening Sunday, 5 October 9:00-9:30 N Yanofsky On the algorithmic informational content of categories 9:30-10:00 S Niefield Par-valued lax functors and exponentiability 10:00-10:30 A Joyal TBA coffee break 11:00-11:30 G Seal Kock-Zoberlein monads from monads on SET 11:30-12:00 D Pronk Translation groupoids and orbifold homotopy theory 12:00-12:30 J Kennison Spectra for Symbolic Dynamics 12:30-1:00 P Freyd TBA

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PhD studentships at Sussex
by Bernhard Reus 26 Sep '08

26 Sep '08

Please distribute widely to students with interest in a PhD: ++++++++++++++++++++++++++++++++++++++++++++++++++++ 2 Phd Studentships in Program Semantics and Verification ++++++++++++++++++++++++++++++++++++++++++++++++++++ available at the University of Sussex (Brighton, UK) to work on an EPSRC funded project the objectives of which is to develop program logics for function pointers and reflective programming principles. Candidates need tp have a good BSc/MSc in Computer Science or Mathematics and should have some interest in programming languages and formal methods. Background in Logic, Semantics, Category Theory, or Type Theory may be useful but is not essential. On the more practical side, experience with theorem provers would be an asset. Students can take on theoretical problems as well as participate in concrete tool development or extension. The studentship (funded by the EPSRC, grant EP/G003173/1) will cover all tuition fees (for EU citizens) and a yearly maintenance grant at the standard rate (currently GBP 12,940). Students will be working under the supervision of Dr Bernhard Reus (PI) and in collaboration with a Post-Doc embedded in the Foundations of Computation Group of the Department. The University is situated in Brighton which is a famous seaside resort at the English south coast, about 50 miles from London (and half an hour from Gatwick Airport). It is renowned for its nightlife, fabulous shops, and cosmopolitan vibe. For further information about the project consult <http://www.informatics.sussex.ac.uk/research/projects/PL4HOStore/> Candidates interested in the studentships should contact: Dr Bernhard Reus (bernhard(a)sussex.ac.uk)

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PhD Program at IMT, Lucca
by Ugo Montanari 25 Sep '08

25 Sep '08

PhD in Lucca, Italy Call for applications: Computer Science and Engineering Deadline December 5th 2008 Classes start in March 2009 Students can apply if they obtain their degrees before December 24, 2008 PhD in Computer Science and Engineering The doctoral Program aims to prepare researchers and professionals with broad training in the foundations of informatics as well as applications to a variety of cutting-edge systems and disciplines. The frontiers of informatics are influencing the paths of other disciplines as well as ordinary life, and are the target of active research on the international scene. Research doctors may work in universities and research centers. They may also take on professional roles and high-profile tasks and responsibilities in both the private and public sectors. 15 positions and 8 scholarships 15 students: no tuition fees + free access to IMT Canteen 8 students: full grants (annual grant amounts +/- 13640 Euros gross) 8 students: free accommodation IMT Distinctive Features -IMT is an international graduate school that promotes cutting-edge research in areas with clear practical relevance, contributing to form international professional elites for business and institutions. -Research and teaching programs at IMT focus on institutional and technological change, the role of organizations and markets in economic systems, the analysis of complex systems in social sciences, computer science and engineering. -IMT aims to recruit students with high potential in a fast-moving global environment where research institutes and universities compete to attract resources and human capital. To do so, IMT uses international selection standards and seeks candidates from all around the globe. -The IMT community is the result of a lively interaction of students and scholars, building upon the campus system and residential services provided by the Lucca Foundation for Higher Education and Research. -PhD Courses are held in English and student curricula and performance is continually assessed through rigorous evaluation processes. CSE PhD Program Board Paolo Ciancarini - Bologna Rocco De Nicola - Firenze Carlo Ghezzi - Milano Luciano Lenzini - Pisa Ugo Montanari - Pisa, Coordinator Antonio Prete - Pisa IMT http://www.imtlucca.it/http://www.imtlucca.it/ is an International Graduate School Founded by: LUISS Guido Carli, Rome Politecnico di Milano Sant'Anna School of Advanced Studies University of Pisa Lucca Foundation for Higher Education and Research Online applications only at: http://www.imtlucca.it/phd_programs/call_for applications/index.php -- @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ Prof. Ugo Montanari Phone: +39 050 2212721 Dipartimento di Informatica Fax: +39 050 2212726 Universita' di Pisa Email: ugo(a)di.unipi.it Largo Bruno Pontecorvo, 3 Address changed recently I-56127 Pisa, Italy http://www.di.unipi.it/~ugo/ugo.html @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

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