*(unknown)@ 2022-12-29 22:47 Valeria de Paiva0 siblings, 0 replies; 20+ messages in thread From: Valeria de Paiva @ 2022-12-29 22:47 UTC (permalink / raw) To: Categories (mailing list) Dear all, It is a pleasure to invite you to the second edition of the Brazilian Meeting on Category Theory, which takes place 20-24th March 2023 at IME, USP, São Paulo, Brazil. This meeting follows the highly successful First Brazilian Meeting on Category Theory in 2021 https://encontrocategorico.mat.br/I/. This edition will be in person with a live broadcast on YouTube. More details on the site of the event https://encontrocategorico.mat.br. Valeria, Hugo Mariano, Ana Luiza Tenorio for the Organization -- Valeria de Paiva http://vcvpaiva.github.io/ https://topos.institute/ http://www.cs.bham.ac.uk/~vdp/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2021-02-19 15:50 Marco Grandis0 siblings, 0 replies; 20+ messages in thread From: Marco Grandis @ 2021-02-19 15:50 UTC (permalink / raw) To: categories This book is being published, and scheduled for March 2021: M. Grandis Manifolds and Local Structures. A general theory World Scientific Publishing Co., xii + 361 pages, 2021. - Info at WS: https://www.worldscientific.com/worldscibooks/10.1142/12199 - Downloadable Introduction https://www.worldscientific.com/doi/epdf/10.1142/9789811234002_0001 ________ Local structures are studied as symmetric enriched categories on ordered categories of partial morphisms; their morphisms are defined as 'compatible profunctors'. This follows a line presented and developed in 1988-90 (whose main sources are cited in the Preface, below): - MG, Manifolds as enriched categories, in: 'Categorical Topology', Prague 1988, pp.358-368, World Scientific Publishing Co., 1989. - MG, Cohesive categories and manifolds, Ann. Mat. Pura Appl. 157 (1990), 199-244. Downloadable: https://link.springer.com/article/10.1007/BF01765319 The main basis of enrichment is called a 'cohesive e-category', or 'e-category' for short. Later, this structure has been re-introduced under the name of 'restriction category' and equivalent axioms. ________ from the PREFACE Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework. An 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on. This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus. Technically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings. This approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis. ________ Marco Grandis [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2019-07-20 7:28 Marco Grandis0 siblings, 0 replies; 20+ messages in thread From: Marco Grandis @ 2019-07-20 7:28 UTC (permalink / raw) To: categories The following article is downloadable: Marco Grandis - George Janelidze, From torsion theories to closure operators and factorization systems, Categ. Gen. Algebr. Struct. Appl., in press. Downloadable from CGASA: http://cgasa.sbu.ac.ir/article_87116.html Abstract. Torsion theories are here extended to categories equipped with an ideal of ‘null morphisms’, or equivalently a full subcategory of ‘null objects’. Instances of this extension include closure operators viewed as generalised torsion theories in a ‘category of pairs’, and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15]. Regards Marco and George [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2017-02-16 16:43 Jean Benabou0 siblings, 0 replies; 20+ messages in thread From: Jean Benabou @ 2017-02-16 16:43 UTC (permalink / raw) To: Categories Dear Steve, I can understand you don't like my question. Some of the answers I received prove that other mathematicians I respect approve of it, have thought about, and have given partial answers to it. If you have any objections, take a stand and give MATHEMATICAL reasons for your objections. All you say is; > I'm saying the same can happen in mathematics. Prove that it DID happen in my question! By the way, I'm no zoologist but, by fishing through your mails, I found a big gap in your refutation. Neither in your mails nor in Fred's did I find any reference to the octopus. If there is any good reason for this omission, mathematical OR zoological, please make it public and justify it. All the best, Jean Le 14 févr. 17 à 09:48, Steve Vickers a écrit : > Dear Fred, > > A good answer, but my point was that it was a bad question. > > You see this once you start pressing at the details. Are seals and > turtles fish? No, but on your definition it depends on whether > flippers count as legs or not. What about sea snakes? Obviously not > - they're snakes, that just happen to live in the sea. But then eels > do seem a bit more fishy. > > A meticulous zoologist would start piling on the subclauses to pin > it down more precisely, but we know that that does not actually > refine our understanding of zoology. It just amplifies the > misconceptions underlying the original question. > > > > All the best, > > Steve. > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2016-04-11 8:35 Timothy Porter0 siblings, 0 replies; 20+ messages in thread From: Timothy Porter @ 2016-04-11 8:35 UTC (permalink / raw) To: categories Dear all, My old e-mail account in Bangor will be dying shortly. My new address will be t.porter.maths@gmail.com Thank you, Tim [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2011-08-14 20:08 claudio pisani0 siblings, 0 replies; 20+ messages in thread From: claudio pisani @ 2011-08-14 20:08 UTC (permalink / raw) To: categories Dear categorists (and topologists), it is known (Clementino, Hofmann, Tholen, Richter, Niefield...) that perfect maps p:X->Y are exponentiable in Top/Y, and that the same holds for local homeomorphisms h:X->Y. Question: is it true that 1) p=>h is a local homeomorphism 2) h=>p is a perfect map? The conjecture is suggested by the following observations: A) it holds both for Y = 1 (compact and discrete space) and for subspaces inclusion (closed and open parts) B) the analogy between perfect maps and local homeomorphisms with discrete (op)fibrations (via convergence or other considerations) and the fact that 1) and 2) above hold in Cat/Y: if p is a discrete fibration and h is a discrete opfibration then p=>h is itself a discrete opfibration (and conversely). Best regards, Claudio [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2010-06-29 7:29 Erik Palmgren0 siblings, 0 replies; 20+ messages in thread From: Erik Palmgren @ 2010-06-29 7:29 UTC (permalink / raw) To: categories Stockholm University announces a position as Professor in Mathematical Logic within the Department of Mathematics Ref nr SU 611-1310-10. Deadline for application: September 15, 2010. Subject: Mathematical logic Subject description: The subject comprises both the logical study of the deductive structure of mathematics, and the mathematical study of formal logical systems. In addition, it deals with the use of logic in computer science. Main tasks: Research, teaching, supervision, together with administrative tasks at the department and the faculty. Required qualifications: To qualify for employment as professor the applicant should have demonstrated both scientific and teaching proficiency. Required qualifications are: * Documented scientific proficiency at a high international level * Documented teaching proficiency. The applicant must have the ability to collaborate as well as the competence and qualities needed to carry out the employment tasks successfully. Assessment criteria: In the appointment process most weight will be given to scientific proficiency. Second most weight will be given to teaching proficiency. Weight will also be given to administrative proficiency, proficiency in developing and leading an organisation, as well as proficiency in interacting with the rest of society. Additional information: The position holder is expected to work at developing the relations between the Mathematics Department and theoretical computer science at NADA and other institutions in the Stockholm area. Since most professors at the Faculty of Science are men, applications from women are particularly welcome. Further information about the position can be obtained from professor Mikael Passare, telephone +46 (0)8 16 45 46, e-mail: passare@math.su.se or professor Tom Britton, telephone +46 (0)8 16 45 34, e-mail: tom.britton@math.su.se. Administrative coordinator Carina Nymark, telephone +46 (0)8 16 17 67, e-mail: carina.nymark@science.su.se will provide further information about the application and appointment procedure if required. Trade union representatives: Bo Ekengren (SACO), Lisbeth HÃ¤ggberg (FackfÃ¶rbundet ST) telephone +46 (0)8 16 20 00 (switchboard) and Gunnar Stenberg (SEKO) telephone +46 (0)70-316 43 41. Guidelines for the application are given in the Template for application for employment and for promotion to the rank of professor or senior lecturer at Stockholm University. The template and other relevant documents including Rules of Employment for the hiring of Teachers can be downloaded from www.su.se/nyanstallning or be provided by the administrative coordinator. It is the responsibility of the applicant to ensure that the application follows the template and that it is submitted before application deadline. In order to apply for this position you are requested to use the Stockholm University webbased application form. You will find the form in the appropriate announcement at www.su.se/ledigaanstallningar and www.su.se/english/about/vacancies Further information Stockholm University: www.su.se/english Templates and rules regarding employment: www.su.se/nyanstallning Department of Mathematics: www.math.su.se You are welcome to submit your application, quoting ref no SU 611-1310-10 no later than September 15, 2010. Disclaimer: In case of discrepancy between the Swedish original and the English translation of the job announcement, the Swedish version takes precedence ------- The original announcement can be found here http://www.math.su.se/content/1/c6/08/19/02/logiken.pdf http://www.math.su.se/pub/jsp/polopoly.jsp?d=14714&a=81902 [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2009-11-19 23:25 claudio pisani0 siblings, 0 replies; 20+ messages in thread From: claudio pisani @ 2009-11-19 23:25 UTC (permalink / raw) To: categories 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/ ] ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2009-04-29 15:27 Unknown0 siblings, 0 replies; 20+ messages in thread From: Unknown @ 2009-04-29 15:27 UTC (permalink / raw) <cat-dist@mta.ca> Envelope-to: categories-list@mta.ca Delivery-date: Fri, 02 Jul 2004 07:47:32 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BgLYe-0005gZ-00 for categories-list@mta.ca; Fri, 02 Jul 2004 07:46:16 -0300 Date: Thu, 1 Jul 2004 06:36:51 -0400 (EDT) From: Michael Barr <barr@barrs.org> X-X-Sender: barr@triples.math.mcgill.ca To: <categories@mta.ca> Subject: categories: Re: Grothendieck bio? In-Reply-To: <20040630174359.50998.qmail@web52607.mail.yahoo.com> Message-ID: <Pine.LNX.4.44.0407010625500.22767-100000@triples.math.mcgill.ca> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 I do not think that anyone has written a biography of AG, but he has written an autobiography, called Recoltes et semailles (Reapings and Sowings--the order is intentionally backwards). It is not publicly available (not published) but someone has, I understand, done a Russian translation that is. There is also a (very) partial English translation that is an ongoing project that requires money to proceed. Thus if you want to read it, you have to send cash to the translator, Roy Lisker. See his web page, http://www.fermentmagazine.org/, for more details. I cannot vouch for the quality of the translation, but I disagree with him on how to translate the title. I think he called it Harvests and Sowings, which clanks on my ear. He says his French is better than mine, which I won't argue, but my wife agrees with me and she is a professional French to English translator. Besides we are not arguing over the meaning, but the best sounding English. Be that as it may, it is the best you can do unless you can read it in Russian (which I assume from your name you can). Sorry, I don't know a source for that. On Wed, 30 Jun 2004, Galchin Vasili wrote: > Hello, > > Does anybody know of a Grothendieck biography? For > me many times it is helpful to read a bio to the > historical development of a person's work. > > Thanks in advance, Bill Halchin > > ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2009-04-29 15:27 Unknown0 siblings, 0 replies; 20+ messages in thread From: Unknown @ 2009-04-29 15:27 UTC (permalink / raw) <cat-dist@mta.ca> Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 Jun 2004 08:40:09 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BV7aG-0000eY-00 for categories-list@mta.ca; Tue, 01 Jun 2004 08:37:32 -0300 Mime-Version: 1.0 (Apple Message framework v613) To: categories@mta.ca Message-Id: <CBA97319-B35F-11D8-A257-000D9367EB64@vuw.ac.nz> Content-Type: multipart/alternative; boundary=Apple-Mail-6-367120408 From: Rob Goldblatt <Rob.Goldblatt@vuw.ac.nz> Subject: categories: preprint on behavioural covarieties Date: Tue, 1 Jun 2004 12:08:22 +1200 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain;charset=ISO-8859-1;format=flowed Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 A preprint of a paper entitled "A comonadic account of behavioural covarieties of coalgebras" is available for downloading as a pdf file from www.mcs.vuw.ac.nz/~rob Rob Goldblatt ABSTRACT: A class K of coalgebras for an endofunctor T on the category of sets is=20= a behavioural covariety if it is closed under disjoint unions and=20 images of bisimulation relations (hence closed under images and domains=20= of coalgebraic morphisms, including subcoalgebras). K may be thought of=20= as the class of all coalgebras that satisfy some computationally=20 significant property. In any logical system suitable for specifying=20 properties of state-transition systems in the Hennessy-Milner style,=20 each formula will define a class of models that is a behavioural=20 variety. Assume that the forgetful functor on T-coalgebras has a right adjoint,=20= providing for the construction of cofree coalgebras, and let G^T be the=20= comonad arising from this adjunction. Then we show that behavioural=20 covarieties K are (isomorphic to) the Eilenberg-Moore categories of=20 coalgebras for certain comonads G^K naturally associated with G^T.=20 These are called pure subcomonads of G^T, and a categorical=20 characterization of them is given, involving a pullback condition on=20 the naturality squares of a transformation from G^K to G^T. We show that=A0 there is a bijective correspondence between = behavioural=20 covarieties of T-coalgebras and isomorphism classes of pure subcomonads=20= of G^T. =20= ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2009-04-29 15:27 Unknown0 siblings, 0 replies; 20+ messages in thread From: Unknown @ 2009-04-29 15:27 UTC (permalink / raw) <cat-dist@mta.ca> Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 May 2004 08:19:25 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BKxk4-0002sJ-00 for categories-list@mta.ca; Tue, 04 May 2004 08:05:40 -0300 Date: Mon, 3 May 2004 22:07:26 +0200 From: "Int. Center for Computational Logic" <cladv@iccl.tu-dresden.de> Message-Id: <200405032007.i43K7QjN015970@spock.inf.tu-dresden.de> To: categories@mta.ca Subject: categories: ICCL Summer School 2004 - Final Call Reply-To: cl-adverts@janeway.inf.tu-dresden.de Sender: cat-dist@mta.ca Precedence: bulk Status: O X-Status: X-Keywords: X-UID: 1 ICCL Summer School 2004 Proof Theory and Automated Theorem Proving ------------------------------------------ PCC Workshop 2004 ------------------------------- Technische Universitaet Dresden June 14-25, 2004 <http://www.iccl.tu-dresden.de/events/SA-2004> Call for Participation ---------------------- This two-week meeting consists of two integrated parts, a summer school and a workshop, aimed at graduate students and researchers. The themes for the summer school are proof theory and automated theorem proving, the workshop is about proof, computation and complexity. As in the summer schools at TU Dresden in 2002 and 2003 and in the previous editions of the PCC workshop, people from distinct but communicating communities will gather in an informal and friendly atmosphere. We ask for a participation fee of 200 EUR. We request registration before May 10, 2004; please send an email to <mailto:PTEvent@ICCL.TU-Dresden.DE>, making sure you include a very brief bio (5-10 lines) stating your experience, interests, home page (if available), etc. It will be possible for some students to present their work: please indicate in your application if you would like to do so and give us some information about your proposed talk. We will select applicants in case of excessive demand. A limited number of grants covering all expenses is available, please indicate in your application if the only possibility for you to participate is via a grant. Applications for grants must include an estimate of travel costs and they should be sent together with the registration. We will provide assistance in finding an accommodation in Dresden. Week 1, June 14-17: courses on Term Rewriting Systems Franz Baader (TU Dresden) Deep Inference and the Calculus of Structures Alessio Guglielmi (TU Dresden) Game Semantics and Its Applications C.-H. L. Ong (Oxford) On June 14 Prof Wolfgang Bibel will give an invited lecture June 17-19: workshop For more details, please consult the workshop web page <http://www1.informatik.unibw-muenchen.de/Birgit/pcc04.html> Week 2, June 21-25: courses on Deduction Modulo Claude Kirchner (Loria & INRIA, Nancy) Logic Considered as a Branch of Geometry Francois Lamarche (Loria & INRIA, Nancy) Proofs as Programs Michel Parigot (CNRS - Universite' Paris 7) Automated Reasoning for Substructural Logics John Slaney (NICTA, Canberra and Australian National University) Automated Theorem Proving for Classical Logics Andrei Voronkov (Manchester) Venue ----- Dresden, on the river Elbe, is one of the most important art cities of Germany. You can find world-class museums and wonderful architecture and surroundings. We will organize trips and social events. Organization ------------ This event is organized by the International Center for Computational Logic (ICCL), Paola Bruscoli, Birgit Elbl, Sylvia Epp, Bertram Fronhoefer, Axel Grossmann, Alessio Guglielmi, Steffen Hoelldobler, Reinhard Kahle and Mariana Stantcheva; it is sponsored by Deutscher Akademischer Austausch Dienst (DAAD), under the program `Deutsche Sommer-Akademie', and CoLogNet. Please distribute this message broadly. ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2009-04-29 15:26 Unknown0 siblings, 0 replies; 20+ messages in thread From: Unknown @ 2009-04-29 15:26 UTC (permalink / raw) <cat-dist@mta.ca> Envelope-to: categories-list@mta.ca Delivery-date: Thu, 01 Apr 2004 14:24:46 -0400 Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1B96pj-0006qu-00 for categories-list@mta.ca; Thu, 01 Apr 2004 14:22:31 -0400 From: Todd Wilson <twilson@csufresno.edu> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <16491.20549.171326.902250@localhost.localdomain> Date: Wed, 31 Mar 2004 15:12:05 -0800 To: categories@mta.ca Subject: categories: Re: on the axiom of infinity In-Reply-To: <200403291603.i2TG3UX6000400@saul.cis.upenn.edu> References: <200403291603.i2TG3UX6000400@saul.cis.upenn.edu> Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 1 On Mon, 29 Mar 2004, Peter Freyd wrote: > There's a particular operator that keeps popping up for me. > > In an arbitrary heyting algebra define x << y to mean that not only > is x less than or equal to y, but the value of y -> x is as small > as it can be, that is, y -> x = x. In a complete heyting algebra > define an order-preserving, inflationary unary operation s by > > sx = inf{ y | x << y }. > > E.g.: on a linearly ordered set if { y | x < y } has a least element > then that's what sx is. If there is no smallest element above x, > then sx = x (even without the completeness hypothesis). In > particular, note, there no assertion that x << sx. > > The subobject classifier in an elementary topos is complete in the > relevant sense: s is definable. A quick description of the > construction to follow is that we're going to turn s into the > successor operation on an NNO. > > DIVERSION: The definition I just gave is the first I came across. The > next incarnation for me was when I wanted a measure of the failure of > booleaness. In any topos, *A*, there's a largest subterminator B > with the property that the slice category *A*/B is boolean. But > given any subterminator, U, we have its "closed sheaves", *A*_(U), the > full subcat of objects A such that AxU --> U is an iso. (This is a > subcategory of sheaves for a Lawvere-Tierney topology. Starting with > a space X then Sheaves(X)_(U) may be identified with Sheaves(U'), > where U' denotes the complement of U.) Note that the lattice of > subterminators in *A*_(U) is isomorphic to the interval of > subterminators in *A* from U up. We can define BU to be the > largest subterminator in *A*_(U) such that *A*_(U)/BU is boolean. > The interval of subterminators in *A* from U up to BU is boolean > and in the relevant internal sense, BU is the largest such > subterminator. We can, of course, translate this all to a unary > operation on Omega. > > It's the same operator s. > > When one specializes this to a space X it becomes historically > familiar if we dualize it it to a deflationary operator on closed > subsets. It's the operation that removes isolated points. The very > operation that got Cantor started. Hence the word "historically". I haven't yet digested the rest of Freyd's post, but all of the above, including the notation x << y, the connection with collapsing maximal Boolean intervals, the "historical" connection with Cantor, and a lot more, can be found in a series of papers of Harold Simmons: H. Simmons, "The Cantor-Bendixson analysis of a frame", Seminaire de mathematique pure, Rapport no. 92, Institut de Mathematique Pure, Universite Catholique de Louvain, January 1980. H. Simmons, "An algebraic version of Cantor-Bendixson analysis", in Categorial Aspects of Toplogy and Analysis, pp. 310-323, Springer LNM 915, 1982. H. Simmons, "Near-discreteness of modules and spaces as measured by Gabriel and Cantor", J. Pure and Appl. Alg. 56 (1989), 119-162. H. Simmons, "Separating the discrete from the continuous by iterating derivatives", Bull. Soc. Math. Belg. 41 (1989), 417-463. The operation Freyd is calling s (and the associated relation <<) arose in connection with the so-called Reflection Problem for Frames, namely to characterize those frames that have a reflection into the category of complete Boolean algebras. When such reflections exist, they can be found by iterating the functor A |-> N(A), which freely complements the elements of A (and is also the frame of nuclei on A, ordered pointwise), until it "terminates": A -> N(A) -> N^2(A) -> ... -> N^a(A) -> ... (a in ORD). (These maps are all both mono and epi and are components of natural transformations between iterates of N). A basic result here is that N(A) is Boolean iff x << sx for all x in A. The general reflection problem remains open. -- Todd Wilson A smile is not an individual Computer Science Department product; it is a co-product. California State University, Fresno -- Thich Nhat Hanh ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2006-03-16 2:08 jim stasheff0 siblings, 0 replies; 20+ messages in thread From: jim stasheff @ 2006-03-16 2:08 UTC (permalink / raw) To categories@mta.ca Subject: categories: Re: cracks and pots <3618C00E-DF36-4BD9-9BC3-A51AB6D1D422@mac.com> In-Reply-To: <3618C00E-DF36-4BD9-9BC3-A51AB6D1D422@mac.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 62 For that remember (if any are as old as I) matrices good, groups bad the gruppenpest jim Krzysztof Worytkiewicz wrote: > The blog in question is indeed more than dubious. Besides the > "scientific" manicheism (group good, monoid bad...), what to think > about ranking countries according to a "civilization index"? The > blogger also claims he was mastering differential geometry and > particle physics at age of 15, so he obviously was too busy and > missed the provocative phase. Not a reason however to try to catch it > up as an "adult". > > Cheers > > Krzysztof > > -- my government will categorically deny the incident ever occurred > > > > > ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2006-03-16 2:07 jim stasheff0 siblings, 0 replies; 20+ messages in thread From: jim stasheff @ 2006-03-16 2:07 UTC (permalink / raw) To categories@mta.ca Subject: categories: Re: cracks and pots In-Reply-To: <E1FJfCK-0003LO-EL@mailserv.mta.ca> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 61 > I was aiming at the fact that > there is > a certain trend within category theory (when did it start?) to consistely > give center stage to anything that claims to have connections with physics > (in particular string theory). Is this because (it is believed that) the > state of category theory is now so poor (as "evidenced" by the lack of > grants) that they (the organizers of meetings) want to repair this image at > any cost? Also, by so doing, are we not becomeing vulnerable? Are we not > pushing students to work on a certain area on the grounds that it is > fashionable and likely to be funded, even if those students may lack the > motivation and sound background knowledge? I feel that this is dangerous > for > category theory (and mathematics in general), as it may lead (is leading?) > to narrow developments of any subject that is approached with these > objectives in mind. I did point these concerns of mine already, in response > to the posting by Robert MacDawson, whom I also thank for giving me the > opportunity to make clearer what my real concerns are. > Consider instead what happened in algebraic topology in the last century (or in invariant theory of polynomial forms in the previous one): classic internal problems e.g. homotopy groups of spheres ground on and on while the enthusiasm and excitement of `application' motivated problems died with a lack of such problems (I have in mind vector fields on spheres and allsorts of diff geom motivations). > On the subject of what constitutes good mathematics, Ronnie Brown has > pointed out to me a beautiful expose (with Tim Porter) which you can > find in > www.bangor.ac.uk/r.brown/publar.html > I urge you to read it. Exactly - if it's good math, it's not tainted by being invented by physicists. jim > > I end with a quote from the end of David Yetter's posting in reply to mine. > "If (I suspect when) the string theory emperor turns out to have no > clothes, > category theory will suddenly become de rigeur in physics". I share his > optimism. > > > Most cordially, > Marta Bunge > > > > > ************************************************ > 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@mcgill.ca > http://www.math.mcgill.ca/bunge/ > ************************************************ > > > > >> From: "John Baez" <baez@math.ucr.edu> >> To: categories@mta.ca >> Subject: categories: Re: cracks and pots >> Date: Tue, 14 Mar 2006 11:56:09 -0800 (PST) >> >> Hi - >> >> > I just came across the following pages >> > >> > http://motls.blogspot.com/2004/11/category-theory-and-physics.html >> > http://motls.blogspot.com/2004/11/this-week-208-analysis.html >> > >> > written by Lubos Motl, a physicist (string theorist). Some of you may >> find >> > these articles interesting and probably revealing. >> > >> > Are we category theorists as a whole going to quietly accept getting >> > discredited by a minority of us presumably applying category theory to >> > string theory? >> >> I can't tell if you're kidding. I'll assume you're not. >> >> There's nothing wrong with applying category theory to string theory. >> The papers by Michael Douglas and Paul Aspinwall cited above by Motl >> are some nice examples of using derived categories to study D-branes. >> >> Further examples: the Moore-Seiberg relations turn out to be little >> more than the definition of a balanced monoidal category, and the >> Segal-Moore axioms for open-closed topological strings are nicely >> captured using category theory here: >> >> http://arxiv.org/abs/math.AT/0510664 >> >> There were a lot of nice talks on the borderline between category >> theory and string theory at the Streetfest. >> >> Perhaps more to the point, Lubos Motl is famous for his heated >> rhetoric. He doesn't like me, or anyone else who criticizes >> string theory. The articles you mention above are mainly reactions >> to my This Week's Finds. >> >> He's actually being very gentle - for him. He even says "the >> role of category theory can therefore be described as a `progressive >> direction' within string theory". >> >> I'm sure you'll all be pleased to know that. :-) >> >> > It is surely not too late to react and point out that this is >> > not what (all of) category theory is about. >> >> I would urge everyone not to react - at least, not until they are >> well aware of what a discussion with him is like. See his blog >> and his comments on Peter Woit's blog if you don't understand what >> I mean. For example: >> >> http://pitofbabel.org/blog/?p=51 >> >> > Please give a thought about what >> > we, as a community, can urgently do to repair this damaging impression. >> >> Since Motl's personality is well known, any damage will be minimal. >> I think we should relax and take it easy. >> >> Best, >> jb >> >> >> >> >> >> >> >> > > > ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2006-03-16 1:58 jim stasheff0 siblings, 0 replies; 20+ messages in thread From: jim stasheff @ 2006-03-16 1:58 UTC (permalink / raw) To categories@mta.ca Subject: categories: Re: cracks and pots In-Reply-To: <E1FJIWr-0003u8-D2@mailserv.mta.ca> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 60 Marta Bunge wrote: > > I was trying to elicit an open response from those who *do* know about the > value (or lack of it) of categorical string theory. In particular, I would > like to have an answer to this question. Why is it that anything which even > remotedly claims to have applications to physics (particularly string > theory) is > given (what I view as) uncritical support in our circles? > > Best, > Marta > It's not so much the applications that seduce some of us but rather the *new* structures the physicists suggest that turn out to have neat mathemaical, e.g. categorical, aspects. e.g quantum groups jim ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2006-03-16 1:53 jim stasheff0 siblings, 0 replies; 20+ messages in thread From: jim stasheff @ 2006-03-16 1:53 UTC (permalink / raw) To categories@mta.ca Subject: categories: Re: cracks and pots References: <E1FIviW-0000Ji-JW@mailserv.mta.ca> <f5f388bc651623725f56290be616e370@math.ksu.edu> In-Reply-To: <f5f388bc651623725f56290be616e370@math.ksu.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 59 Mostly well said, David I would only modify/deform ;-) what you say by doubting therte are that many physicists who are anti-cat theory (not pro-) but watch out once some leader of the school adopts it the school will follow - much faster than if they were mathematicians jim David Yetter wrote: > Dear Marta, > > My reaction to the blog posts you cite is that this is a sting theorist > holding > his breath and refusing to learn category theory. My guess is that Motl > wouldn't > want to learn the heavily categorical formulations of mirror symmetry > that Yan > Soibelman uses, even though they are motivated by string theory. > Basically > categorical ideas aren't part of the standard bag of tricks physicists > use (even > though they often give much more elegant, concise, and insightful > formulations of some of those tricks), and the proverb about 'old dogs' > and > 'new tricks' applies to physicists as well. > > His attack on Baez is fairly standard stuff: in the mode of "string > theory > is the theory of nature, so we don't want to think about alternatives > like > loop quantum gravity." It is a polemical defense of a scientific > theory that > hasn't produced a testable prediction in the 40 plus years since its > inception, > and worse than that, unless one adds bells and whistles to fix it (in > the manner > of 'gaseous Vulcan' or Ptolemaic epicycles), predicts the existence > of a massless scalar field *not observed in nature*. It really has > nothing at > all to say about category theory, which is after all a mathematical > theory > which stands irrespective of its extra-mathematical applications. > > Categorical ideas are absolutely central to several competitors to > string theory: > the Barrett-Crane model of quantum gravity (and to a lesser > extent 'loop quantum gravity' with which the BC model is often > conflated) > and Connes' recovery of the Standard Model from non-commutative geometry > (a part of mathematics which has obliged reluctant mathematicians to > think about > categorical ideas deeper than they originally were comfortable with). > There is nothing > cracked or crackpot about either. > > It is simply a fact we have to live with that our subject has found > legitimate uses > in physics, but uses which are unpopular with the dominant school of > physics in > the North America. If (I suspect when) the string theory emperor turns > out > to have no clothes, category theory will suddenly become de rigeur in > physics. (As it should, since categorical expressions of physical > ideas are the logical conclusion of 20th century physics drive to > express > everything in coordinate-free terms.) > > Best Thoughts, > David Yetter > > > > > > > > > > On 12 Mar 2006, at 17:29, Marta Bunge wrote: > >> Hi, >> >> I just came across the following pages >> >> http://motls.blogspot.com/2004/11/category-theory-and-physics.html >> http://motls.blogspot.com/2004/11/this-week-208-analysis.html >> >> written by Lubos Motl, a physicist (string theorist). Some of you may >> find >> these articles interesting and probably revealing. >> >> Are we category theorists as a whole going to quietly accept getting >> discredited by a minority of us presumably applying category theory to >> string theory? It is surely not too late to react and point out that >> this is >> not what (all of) category theory is about. Please give a thought >> about what >> we, as a community, can urgently do to repair this damaging impression. >> Unless we are prepared to wait until things change by themselves >> within our >> lifetime. >> >> >> Hopefully disturbing your weekend, >> Cordially, >> 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@mcgill.ca >> http://www.math.mcgill.ca/bunge/ >> ************************************************ >> >> >> >> ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 2000-02-12 17:23 James Stasheff0 siblings, 0 replies; 20+ messages in thread From: James Stasheff @ 2000-02-12 17:23 UTC (permalink / raw) To: dmd1, categories As of some notes from 1996, it was an open question as to how to make a closed model category from coalgebras which as dg modules are flat over the ground ring one problem: the naive cokernel is no longer flat .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 1998-05-24 4:31 Ralph Leonard Wojtowicz0 siblings, 0 replies; 20+ messages in thread From: Ralph Leonard Wojtowicz @ 1998-05-24 4:31 UTC (permalink / raw) To: categories On pages 29--30 of "Categories for the Working Mathematician," MacLane reveals that "the discovery of ideas as general as [categories, functors and natural transformations] is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: `Category' from Aristotle and Kant, `Functor' from Carnap and `natural transformation' from then current informal parlance." Ideas from writings of Karl Marx are described in "Conceptual Mathematics: A First Introduction to Category Theory," by Lawvere and Schanuel and elsewhere. What orientation or program of study has philosophy given the investigation of mathematical categories? Where could one begin reading to understand this influence? Was selection of "monad" influenced by writings of Leibniz? Thank you for your time. Sincerely, Ralph Wojtowicz ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 1998-05-12 15:09 esik0 siblings, 0 replies; 20+ messages in thread From: esik @ 1998-05-12 15:09 UTC (permalink / raw) To: rrosebrugh >From esik Tue May 12 16:09:55 +0200 1998 remote from inf.u-szeged.hu To: rrosebrugh@mta.ca cc: esik Subject: FICS 2nd announcement Date: Tue, 12 May 1998 16:09:55 +0200 From: Esik Zoltan <esik@inf.u-szeged.hu> Received: from inf.u-szeged.hu by inf.u-szeged.hu; Tue, 12 May 1998 16:09 MET Content-Type: text Content-Length: 4630 Dear Professor Rosebrugh, Would you please forward the attached 2nd announcement of the FICS workshop to the subsribers of categories. Thank you in advance. Yours sincerely, Zoltan Esik ******************************************************************************* ******************************************************************************* ** ** ** F I C S ' 9 8 ** ** ** ** Fixed Points in Computer Science ** ** ** ** A Satellite Workshop to MFCS'98 ** ** ** ** August 27-28, 1998, Brno, Czech Republic ** ** ** ** Second Announcement ** ** ** ******************************************************************************* ******************************************************************************* Aim: Fixed points play a fundamental role in several areas of computer science, and the construction and properties of fixed points have been investigated in many different frameworks. The aim of the workshop is to provide a forum for researchers to present their results to those members of the computer science community who study or apply the fixed point operation in the different fields and formalisms. Topics: Construction and reasoning about properties of fixed points, categorical, metric and ordered fixed point models, continuous algebras, relation algebras, fixed points in process algebras and process calculi, regular algebra of finitary and infinitary languages, formal power series, tree automata and tree languages, infinite trees, the mu-calculus and other programming logics, fixed points in relation to dataflow and circuits, fixed points and the lambda calculus. Invited lectures: A. Arnold (Bordeaux): Boolean mu-calculus and its relations with model-checking and games J. W. de Bakker (Amsterdam): Fixed points in metric semantics Y. N. Moschovakis (Los Angeles/Athens): Fair, non-deterministic recursion in higher types (tentative) Program Committee: R. Backhouse (Eindhoven) S. L. Bloom (Hoboken) C. Boehm (Rome) R. De Nicola (Florence) Z. Esik (Szeged, chairman) P. Freyd (Philadelphia) I. Guessarian (Paris) D. Kozen (Cornell) W. Kuich (Vienna) M. Mislove (Tulane) R. F. C. Walters (Sydney) Contact person: Zoltan Esik Dept. of Computer Science Jozsef Attila University P.O.B. 652 6701 Szeged, Hungary e-mail: fics@inf.u-szeged.hu phone: ++36-62-454-289 fax: ++36-62-312-292 Paper submission: Authors are invited to send three copies of an abstract not exceeding three pages to the PC chair. Electronic submissions in the form of uuencoded postscript file are encouraged and can be sent to fics@inf.u-szeged.hu. Submissions are to be received before May 25, 1998. Authors will be notified of acceptance by June 25, 1998. Proceedings: Preliminary proceedings containing the abstracts of the talks will be available at the meeting. Publication of final proceedings as a special issue of Theoretical Informatics and Applications depends on the number and quality of the papers. The workshop will be organised at the same place as the federated MFCS'98/CSL'98 conference and care will be taken that participants of the workshop can attend invited talks of the MFCS and CSL conferences. No special registration fee is required for participants who also register for MFCS'98 or CSL'98 and have a presentation at the workshop. Other workshop participants registered for MFCS'98 or CSL'98 will be requested to pay a small fee for the preliminary proceedings. Registration only for the workshop is also possible--expenses for fee, accommodation, and basic meals are very modest. Registration information can be found on the MFCS web page at http://www.fi.muni.cz/mfcs98. Organising Committee: L. Bernatsky (Szeged) A. Kucera (Brno) T. Szeles (Szeged) More information is available at the following web sites: http://www.inf.u-szeged.hu/fics/ http://www.cs.stevens-tech.edu/CFP/FICS/ ^ permalink raw reply [flat|nested] 20+ messages in thread

*(unknown)@ 1998-02-15 11:43 esik0 siblings, 0 replies; 20+ messages in thread From: esik @ 1998-02-15 11:43 UTC (permalink / raw) To: categories >From esik Sun Feb 15 12:43:53 +0100 1998 remote from inf.u-szeged.hu To: categories@mta.ca cc: esik Subject: CATS Re: Categorical model for Floyd-Hoare logic Date: Sun, 15 Feb 1998 12:43:53 +0100 From: Esik Zoltan <esik@inf.u-szeged.hu> Received: from inf.u-szeged.hu by inf.u-szeged.hu; Sun, 15 Feb 1998 12:43 MET Content-Type: text Content-Length: 561 > Has there been work on a categorical model for > "while programs" (or,equivalently, assembly > language) and Floyd-Hoare logic? The books E.G. Manes: Predicate Transformer Semantics, Cambridge University Press, 1992 S.L. Bloom and Z. Esik: Iteration theories, Springer, 1993 (see in particular chapter 12 and 14) and the paper S.L. Bloom and Z. Esik: Floyd-Hoare logic in iteration theories, JACM, 38(1991), 887--934 consider such models. The books also contain references to other papers (including papers by Elgot and others). Zoltan Esik ^ permalink raw reply [flat|nested] 20+ messages in thread

end of thread, other threads:[~2022-12-29 22:47 UTC | newest]Thread overview:20+ messages (download: mbox.gz / follow: Atom feed) -- links below jump to the message on this page -- 2022-12-29 22:47 (unknown) Valeria de Paiva -- strict thread matches above, loose matches on Subject: below -- 2021-02-19 15:50 (unknown) Marco Grandis 2019-07-20 7:28 (unknown) Marco Grandis 2017-02-16 16:43 (unknown) Jean Benabou 2016-04-11 8:35 (unknown) Timothy Porter 2011-08-14 20:08 (unknown) claudio pisani 2010-06-29 7:29 (unknown) Erik Palmgren 2009-11-19 23:25 (unknown) claudio pisani 2009-04-29 15:27 (unknown) Unknown 2009-04-29 15:27 (unknown) Unknown 2009-04-29 15:27 (unknown) Unknown 2009-04-29 15:26 (unknown) Unknown 2006-03-16 2:08 (unknown) jim stasheff 2006-03-16 2:07 (unknown) jim stasheff 2006-03-16 1:58 (unknown) jim stasheff 2006-03-16 1:53 (unknown) jim stasheff 2000-02-12 17:23 (unknown) James Stasheff 1998-05-24 4:31 (unknown) Ralph Leonard Wojtowicz 1998-05-12 15:09 (unknown) esik 1998-02-15 11:43 (unknown) esik

This is a public inbox, see mirroring instructions for how to clone and mirror all data and code used for this inbox; as well as URLs for NNTP newsgroup(s).