October 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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Sketches and lattices
by Toby Kenney 29 Oct '08

29 Oct '08

Dear Category Theorists, Does anyone know whether any work has been done on sketches where all diagrams are required to commute - i.e. the models are functors from a poset to the given category. I'm particularly interested in the case where the sketch is in fact a lattice, and where we require every avb--------------a | | | | | | b--------------a^b should be sent to a pullback. Thanks for any pointers you can give. Toby

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Web-based category theory demonstrations
by Jocelyn Paine 28 Oct '08

28 Oct '08

I'd like to announce a selection of Web-based category theory demonstrations that I've put up at http://www.j-paine.org/cgi-bin/webcats/webcats.php . The page contains a number of buttons such as "generate and demonstrate an equaliser" and "generate and demonstrate a limit": clicking on one will generate an example of the construct in the category of finite sets, and display it as a listing of its objects and arrows, and as a diagram. For limits and colimits, the demos generate a small random graph, convert it to a diagram, then compute and display its limit or colimit. Comments would be very welcome. The demos are a bit of an experiment: I had some categorical algorithms lying around from other work, and thought it would be interesting to connect them to the Web. Jocelyn Paine http://www.j-paine.org/

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A Young Research Fellow Position at IMT, Lucca
by Ugo Montanari 27 Oct '08

27 Oct '08

A Young Research Fellow Position at IMT, Lucca, Italy Computer Science and Engineering Deadline December 1st, 2008 IMT Institute for Advanced Studies invites strong candidates active on networking and software systems for global computing, including web data mining and mobile systems, with applications e.g. to service oriented computing, economics and embedded systems, to apply for a Faculty Position at the Assistant Professor or Post-Doctoral Fellow level. Preference will be given to candidates combining in their research fundamental and application oriented aspects. Preference will be given to candidates with a Ph.D. degree (or close to completion), or candidates with experience in formal instruction at the graduate-level. The selected candidate will be appointed for a term of up to three years. The contract may be renewed once for additional 3 years (i.e. six year in total). The remuneration package is competitive at the international level and include generous research funds. Additional benefits may be negotiated with selected applicants. Assistant Professors are senior positions and differ from Post-doctoral Fellows on the basis of experience, scientific curriculum and remuneration. Successful candidates for either type of position will work closely with other young researchers, senior researchers and graduate students, and will have a limited teaching load in the school's graduate program (e.g. one class per year). Application Procedure Applicants are required to fill out the online application form and upload a complete curriculum vitae and one research paper (published or working paper) as PDF files. Please note that you are also required to upload a signed copy of your Identity Document. Online applications only at: http://www.imtlucca.it/faculty/positions/young-research-fellows_positions/c… Candidates are required to indicate if they intend to apply only for one of the two positions offered (Assistant Professor and Post-doctoral Fellow) or for both. Please note that if you apply for both positions you do not need to submit two applications. In addition, at least two letters of reference must be sent as e-mail attachments (preferably in PDF format) to: yrf.opening(a)imtlucca.it or by mail to the following address: Job Openings 2009 - YRF-CSE. IMT Lucca Institute for Advanced Studies Piazza San Ponziano, 6 55100 Lucca - Italy 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 -- @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ 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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Re: collaborative_mathematics_exposition?
by Andre Joyal 25 Oct '08

25 Oct '08

Dear Ricardo, The iBourbaki project is alive and moving. You will hear about it soon. André -------- Message d'origine-------- De: categories(a)mta.ca de la part de Ricardo Andrade Date: jeu. 23/10/2008 12:05 À: categories(a)mta.ca Objet : categories: collaborative mathematics exposition Greetings, Sorry to spam everyone in the list but I was curious whether the ideas for a wiki-style project on exposition of mathematics (which were previously discussed on this mailing list) were going somewhere or being implemented. The reason I am asking is that I am curious/interested in such a project and I was left not understanding what came out of the previous discussion on this list since it just seemed to stop rather abruptly. Thank you, Ricardo k

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collaborative mathematics exposition
by Ricardo Andrade 24 Oct '08

24 Oct '08

Greetings, Sorry to spam everyone in the list but I was curious whether the ideas for a wiki-style project on exposition of mathematics (which were previously discussed on this mailing list) were going somewhere or being implemented. The reason I am asking is that I am curious/interested in such a project and I was left not understanding what came out of the previous discussion on this list since it just seemed to stop rather abruptly. Thank you, Ricardo

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A naive question
by Andre Joyal 21 Oct '08

21 Oct '08

The forgetful functor from groups to monoids has a right adjoint which associates to a monoid its group of invertible elements. I am looking for a general explanation of this observation. It should a consequence of a general result on forgetful functors of a certain kind. Best, andré

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ALICS workshop at LPAR
by geoff＠cs.miami.edu 20 Oct '08

20 Oct '08

----------------------------------------------------- *ALICS* - Applications of Logic in Computer Security LPAR 2008 workshop, November 22, Doha, Qatar ----------------------------------------------------- EXTENDED SUBMISSION DEADLINE - 24th October ----------------------------------------------------- Organizer: Catherine Meadows, NRL Submission deadline: October 24, 2008 Submission: 1-5 pages abstract Web: http://chacs.nrl.navy.mil/projects/ALICS08 Scope: ALICS is intended to be an informal workshop devoted to the applications of logic in computer security. This workshop is intended for presentation and discussion of work in progress and the discussion of emerging and foundational ideas. We are interested in all aspects of the application of logic to computer security. Applications of interest include security policy, access control, security protocols, information flow, but we are also interested in new and as yet untried applications of logic to different areas of computer security. We are also interested in discussion papers that raise fundamental questions and/or suggest new lines of research in this area. Work that has already appeared or is under consideration by other venues is welcome. No formal proceedings is planned, but accepted abstracts will be posted online. Program Committe and Organizers: Catherine Meadows, Naval Research Laboratory, USA (Workshop Organizer) Andreas Bauer, Australian National University, Australia Heiko Mantel, TU Darmstadt, Germany Mike Mislove, Tulane University, USA Dusko Pavlovic, Kestrel Institute (USA) and Oxford University(UK) Luca Vigano, University of Verona, Italy

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Matrices Category
by Hugo Macedo 17 Oct '08

17 Oct '08

Hello I'm trying to study the Category of Matrices but I found almost nothing. Do you know where I can find information about them? More specifically can we consider the tensor product as the product bi-functor? -- Hugo

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