October 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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Conditions for adjoints -- another variant
by robin＠ucalgary.ca 10 Nov '09

10 Nov '09

BTW. Here are some even cleaner conditions .... There is an adjoint between two categories iff there are two object functions F and G (not required to be functors) and For each X \in \X and Y \in \Y there are two functions: #: \X(X,G(Y)) -> \Y(F(X),Y) ---- sharp @: \Y(F(X),Y) -> \X(X,G(Y)) ---- flat (i)' @ and # are inverse @(#(f)) = f and #(@(g)) = g (ii)' @(h k) = @(h) @(#(1) k) and dually #(xy) = #(x @(1)) #(y) Still hoping to find where these all are recorded!! -robin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Manin's interview
by Andre Joyal 01 Nov '09

01 Nov '09

http://www.ams.org/notices/200910 http://www.ams.org/notices/200910/rtx091001268p.pdf [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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CfP: QNET - Oxford - 10/11 Dec
by Ross Duncan 30 Oct '09

30 Oct '09

(apologies for multiple copies) --------------------------------------------------------------------- Call for Contributed Talks QNET Workshop on Foundations of Quantum Computation 10/11 December 2009 Oxford University Computing Laboratory http://wiki.comlab.ox.ac.uk/qnet/ --------------------------------------------------------------------- We are pleased to announce the fourth and final QNET workshop on the Foundations of Quantum Computation. QNET is an EPSRC funded research network on Semantics of Quantum Computation. The purpose of the network is to support interaction and collaboration between UK researchers working on the application of semantic techniques to quantum computation. The workshop will take place on the 10th and 11th of December at the Oxford University Computing Laboratory. The invited speakers of the workshop will be: * Caslav Brukner, University of Vienna * Adrian Kent, University of Cambridge We invite contributed talks of 30 minutes on all areas relevant to the foundations of quantum computation, especially on the application of logic, semantics, types, and categorical techniques to quantum computation. To contribute a talk, please send a title and abstract to qnet.workshop(a)gmail.com. Registration is required, but free; to register email qnet.workshop(a)gmail.com. There will be a workshop banquet at Wolfson College on Thursday the 10th of December. For attendees who are not members of the network, this will cost £30. DATES ------ Deadline for contributions : 9 November 2009 Notification : 13 November 2009 Deadline for Registration: 7 December 2009 Workshop dates: 10-11 December 2009 FUNDING --- Some funding will be available for QNET members to attend the workshop, but because the grant is ending, the budget is limited and it will not be possible to give an open commitment to fully fund all attendance costs as with previous workshops. We will do our best to provide funding in as fair a way as possible, and certainly to prioritize funding for PhD students. Please note that if you want funding form the network you MUST email Ian Mackie at i.mackie(a)sussex.ac.uk in advance. It will not be possible to reimburse expenses otherwise, because the remaining budget will have been allocated. Further information can be found on the workshop webpage: http://wiki.comlab.ox.ac.uk/qnet/ Best wishes, Ross Duncan Jamie Vicary -------- QNET Workshop - 10-11 December 2009 Oxford University Computing Laboratory http://wiki.comlab.ox.ac.uk/qnet/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Marta Bunge's email addresses
by Marta Bunge 29 Oct '09

29 Oct '09

Dear Robert,Please announce the following possibly important message in categories. By some unfortunate coincidence, and without my being aware of, I have not been receiving any mail whatsoever, and for quite some undetermined time, either at my official departmental address, bunge(a)math.mcgill.ca, or at the no longer existing address bunge(a)triples.math.mcgill.ca, listed however as mine in the Editorial Board of the Cahiers de Topologie et Geometrie Differentielle Categoriques. The first problem has now been fixed, and bunge(a)math.mcgill.ca is now a good address for me. I am worried of course about the mail that I have not received in that location since perhaps May 2009. If there has been anything important that any of you has sent me, please send again. The second problem will be fixed by changing the obsolete address bunge(a)triples.math.mcgill.ca in the Cahiers, but only as of January 2010 when the new covers get printed. If anyone (in addition to the two cases that I now know about) has submitted a paper to me using the current Cahiers address, please resend but to bunge(a)math.mcgill.ca (without the "triples"). You could also use my McGill University official address, that is, marta.bunge(a)mcgill.ca, which never had any problems. Thank you and apologies for any inconvenience. Marta ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 Office: (514) 398-3810 Home: (514) 935-3618 marta.bunge(a)mcgill.ca http://www.math.mcgill.ca/~bunge/ ************************************************ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Postdoc program 2010 (Foundation "Sciences Mathematiques de Paris")
by Pierre-Louis Curien 28 Oct '09

28 Oct '09

Dear colleagues, The Foundation Sciences Mathematiques de Paris www.sciencesmaths-paris.fr that covers all fields of mathematics as well as (theoretical) computer science, has opened its 2010 programs, including an attractive research chair and a (1 year or 2 years) postdoc programme. Applications that are particularly suited for one of the two research labs of the Foundation (LIAFA and PPS: www.liafa.jussieu.fr and www.pps.jussieu.fr) or/and for one of the research teams of INRIA Rocquencourt associated with the Foundation are welcome. The deadlines for postdoc application is **** December 13, 2009 **** The application procedure is as indicated on the website of the Foundation (English version available). But I can only highly recommend that potential candidates take prior contacts with a member of the hosting laboratory or team. Only candidates with a clear research fit, and a high research profile may have a chance to win this tough competition, given its broad scope! Don't hesitate to contact me or one of my colleages in Paris 7 University for further details or advice. For potential applications to the research chair position, please contact me! Best regards, Pierre-Louis [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Conditions for adjoints
by robin＠ucalgary.ca 25 Oct '09

25 Oct '09

(Apologies to those who received the earlier type mashed version ...) Jeremy Dawson and I were discusing whether one can express the conditions for an adjoint without requiring functors ... this is what we came up with: There is an adjoint between two categories if and only if there are object functions F and G (not functors) and for each X in \X and Y in \Y there are functions: #: \X(X,G(Y)) -> \Y(F(X),Y) ---- sharp @: \Y(F(X),Y) -> \X(X,G(Y)) ---- flat between the homsets such that (1) @(#(1)) = 1 and dually #(@(1)) = 1 (inverse on identities) (2) @(1) @(#(1) #(f)) = f and dually #(@(g) @(1)) #(1) = g (3) @(#(f @(1)) h k) = f @(h) @(#(1) k) and dually #(x y @(#(1) z)) = #(x @(1)) #(y) z. I find it hard to believe that such conditions have not been recorded. Does anyone have a reference or similar conditions which do not require functors? -robin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Literature question: "Category theory" and "epigenetics"
by Steve Stevenson 24 Oct '09

24 Oct '09

Is anyone aware of work in this area? Epigenetics is fairly new, so it is possible that such might have been done in biochemistry or genetics. Thanks in advance. Steve === Dr. D. E. Stevenson, School of Computer Science 315 McAdams Hall, Clemson University 864-656-5880 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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