November 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

1 1

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/ ]

5 4

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 ************************************************************

2 1

Dangerous knowledge
by Joyal, André 13 Dec '09

13 Dec '09

21 40

Question on adjoints
by claudio pisani 30 Nov '09

30 Nov '09

[Note from moderator: resent with a subject line] Dear categorists, this is a remark about the very first proposition in the "elephant", followed by some questions. Lemma 1.1.1 says: If F is left adjoint to G : D --> C and there is a natural isomorphism FG --> 1_D (not necessarily the counit), then G is full and faithful. The proof sketched there uses the transfer of the comonad structure via the given iso. Here is an alternative and more explicit proof: 1) By the hypothesis, there are natural isomorphisms D(-,-) = D(FG-,-) = C(G-,G-) so that the bimodule C(G-,G-) : D -|-> D has a biuniversal element u(x) : Gx --> Gx, for any x in D. 2) By the right and left universality, u(x) is right and left invertible, so that it is an iso. 3) (Right) universality of u(x) gives bijections D(x,y) --> C(Gx,Gy) ; f |--> Gf.u(x) which factor through the arrow map of G and the composition by u(x); since the latter is a bijection by 2), the same holds for the former. Questions: 1) Is this proof correct? Is it "essentially the same" of the one in the book? 2) Anyway, the result states that in this case to say that "there is a natural isomorphism" is equivalent to say that "the canonical natural transformation (the counit) is an iso". Since many important categorical "exactness" conditions are expressed by requiring that some canonical transformations are iso (e.g. distributivity, Frobenius reciprocity and so on) one may wonder if also in these cases it is enough to require the existence of a natural isomorphism. I suppose that the answer is negative, but are there simple counter-examples? Best regards, Claudio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

4 3

QNET - final call for participation - Oxford 10/11 December
by Ross Duncan 27 Nov '09

27 Nov '09

(apologies for multiple copies) --------------------------------------------------------------------- Final Call for Participation QNET Workshop on Foundations of Quantum Computation 10/11 December 2009 Oxford University Computing Laboratory http://wiki.comlab.ox.ac.uk/qnet/ --------------------------------------------------------------------- We invite participants for 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, however participation in the workshop is open to anyone, not just UK researchers. 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 In addition, there will be 19 contributed talks, covering a broad range of topics related to the foundations of quantum computation, ranging from Bell inequalities to Chu spaces. The full programme is available from the workshop website. Registration is required, but free; to register email qnet.workshop(a)gmail.com . The QNET workshop is co-located with QUOXIC, a smaller quantum computing workshop, taking place on the afternoon of the 9th of December. QNET participants are welcome to attend the QUOXIC meeting as well -- see http://qunat.org/quoxic/ for the programme. DATES ------ Deadline for Registration: 7 December 2009 Workshop dates: 10-11 December 2009 Further information can be found on the workshop webpage: http://wiki.comlab.ox.ac.uk/qnet/ Best wishes, Ross Duncan -------- 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/ ]

1 0

Re: question on pseudomorphisms
by burroni＠math.jussieu.fr 25 Nov '09

25 Nov '09

Dear Steve, Thank you for your precious informations (I have never read the article "two-dimensional ..."). But my interest is really in the case of non necessarily 2-monad over Cat and I am convinced that the adjonction j -| i exists, with or without coherences (for the pseudomorphisms). Best regards, Albert Steve Lack <s.lack(a)uws.edu.au> a écrit : > Dear Albert, > > In the case where T is a 2-monad with rank, and the pseudomorphisms are (as > usual) assumed to be coherent, then this was proved by Blackwell-Kelly-Power > in the paper 2-dimensional monad theory. (Here "rank" means that the > 2-functor T preserves alpha-filtered colimit for some alpha - without some > such assumption, I don't know how you can prove that the left adjoint j > exists, and I suspect it does not.) > > If T has rank but pseudomorphisms are not required to be coherent, then the > adjoint j will exist, but the morphism A-->ijA need not be an equivalence > (take the identity monad for example). > > If T is not even a 2-monad then I'm not sure what coherence of the 2-cells > would mean, but in any case there will be problems. > > Regards, > > Steve Lack. > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

question on pseudomorphisms
by burroni＠math.jussieu.fr 24 Nov '09

24 Nov '09

Dear all, Has the following question been already studied and, if it is the case (it is my opinion), where ? Let T be a monad on Cat (not necessarily a 2-monad), C the category of T-algebras and C' the catégorie with the same objets but with pseudomorphisms (morphisms up to natural isomorphisms --- eventually with coherences). The inclusion i : C --> C' has a left adjoint j : C' --> C. The question is : for all T-algebra A, is the canonical morphisms m : A --> i(j(A)) an equivalence (of the underlying categories) ? Regards, Albert [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

2 1

Work-In-Progress
by Ellis D. Cooper 24 Nov '09

24 Nov '09

Dear categorists, The publisher has pre-announced my book on amazon.com. Search on "Mathematical Mechanics: From Particle to Muscle." A PDF of the work-in-progress is available on request. Product Description "This unprecedented book offers all the details of the mathematical mechanics underlying state-of-the-art modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. The method is to take advantage of modern mathematical technology - Eilenberg-Mac Lane category theory, Robinson infinitesimal calculus and Kolmogorov probability theory - to examine a succession of distinguishable universes of particles, and continuous, thermodynamic, chemical, and molecular bodies, all with a focus on proofs by algebraic calculation without set theory. Also provided are metaphors and analogies, and careful distinction between representational pictures, mental model drawings, and mathematical diagrams. High school mathematics teachers, undergraduate and graduate college students, and researchers in mathematics, physics, chemistry, and biology may use this integrated publication to broaden their perspective on science, and to experience the precision that mathematical mechanics brings to understanding the muscular mechanism of nearly all animal behavior." Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

CMCS 2010: First call for papers
by A.M.Silva＠cwi.nl 20 Nov '09

20 Nov '09

------------------------------------------------------------------------------ CMCS 2010 First call for papers ------------------------------------------------------------------------------ The Tenth International Workshop on Coalgebraic Methods in Computer Science 26-28 March 2010, Paphos, Cyprus (co-located with ETAPS 2010) http://event.cwi.nl/cmcs10/ 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. The topics of the workshop include, but are not limited to: * the theory of coalgebras (including set theoretic and categorical approaches); * coalgebras as computational and semantical models (for programming languages, dynamical systems, etc.); * coalgebras in (functional, object-oriented, concurrent) programming; * coalgebras and data types; * (coinductive) definition and proof principles for coalgebras (with bisimulations or invariants); * coalgebras and algebras; * coalgebraic specification and verification; * coalgebras and (modal) logic; * coalgebra and control theory (notably of discrete event and hybrid systems). 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. Invited Speakers --------------------- At this tenth meeting the following invited speakers will present overviews of important subareas. * Venanzio Capretta: Coalgebra in functional programming and type theory * Bartek Klin: Operational semantics coalgebraically * Dirk Pattinson: Logic and coalgebra * Ana Sokolova: Probabilistic systems coalgebraically 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. They must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Accepted papers will appear in ENTCS (style files can be found in http://www.entcs.org/) The web-based system EasyChair will be used for submission (http://www.easychair.org/conferences/?conf=cmcs10) After the event, 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. For short submissions, the style file easychair.cls should be used (http://www.easychair.org/coolnews.cgi) The submission (pdf file) is via email: cmcs10(a)cwi.nl. 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 Programme Committee ------------------------ Jiri Adamek (Braunschweig) Alexandru Baltag (Oxford) Luis Barbosa (Braga) Marcello Bonsangue (Leiden) Corina Cirstea (Southampton) Robin Cockett (Calgary) Andrea Corradini (Pisa) Neil Ghani (Glasgow) Peter Gumm (Marburg) Furio Honsell (Udine) Bart Jacobs (Nijmegen, co-chair) Bartek Klin (Cambridge) Clemens Kupke (London) Alexander Kurz (Leicester) Marina Lenisa (Udine) Stefan Milius (Braunschweig) Ugo Montanari (Pisa) Larry Moss (Bloomington) Milad Niqui (Amsterdam) Dirk Pattinson (London) Dusko Pavlovic (Oxford) John Power (Edinburgh) Horst Reichel (Dresden) Grigore Rosu (Urbana) Jan Rutten (Amsterdam, co-chair) Davide Sangiorgi (Bologna) Lutz Schroeder (Bremen) Alexandra Silva (Amsterdam) Hendrik Tews (Nijmegen) Tarmo Uustalu (Tallinn) Yde Venema (Amsterdam) Hiroshi Watanabe (Osaka) James Worrell (Oxford) Organising Committee -------------------------- Bart Jacobs, Milad Niqui (co-chair, CWI), Jan Rutten, Alexandra Silva (co-chair, CWI). Contact ---------- cmcs10(a)cwi.nl . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0