From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6765 Path: news.gmane.org!not-for-mail From: =?ISO-8859-1?Q?Andr=E9_Joyal?= Newsgroups: gmane.science.mathematics.categories Subject: RE: Timelines for category theory: a response to comments Date: Mon, 11 Jul 2011 13:34:59 -0400 Message-ID: Reply-To: =?ISO-8859-1?Q?Andr=E9_Joyal?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=ISO-8859-1; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1310479070 9577 80.91.229.12 (12 Jul 2011 13:57:50 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 12 Jul 2011 13:57:50 +0000 (UTC) Cc: categories , janelg@telkomsa.net To: ronnie.profbrown@btinternet.com Original-X-From: majordomo@mlist.mta.ca Tue Jul 12 15:57:46 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QgdT8-0000xv-1l for gsmc-categories@m.gmane.org; Tue, 12 Jul 2011 15:57:46 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57933) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1QgdQm-00013R-5z; Tue, 12 Jul 2011 10:55:20 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QgdQl-00067P-Fb for categories-list@mlist.mta.ca; Tue, 12 Jul 2011 10:55:19 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6765 Archived-At: Dear Ronnie and George, The timeline of a field is a time ordered list of the significant =20 developments of this field. Of course, one may disagree on what is significant. A timeline is inherently cahotic, since many developements are =20 inherently unpredictable. Some developements are influenced by what is happening outside the =20 field. It would be wrong to organise a timeline as if it were a plan for a =20 course in category theory. Of course, we could have a timeline for topos theory, or for any sub-=20= discipline of category theory. Best,-Andr=E9 -------- Message d'origine-------- De: Ronnie Brown [mailto:ronnie.profbrown@btinternet.com] Date: dim. 10/07/2011 13:03 =C0: categories@mta.ca Cc: George Janelidze Objet : categories: Timelines for category theory: a response to =20 comments Dear Colleagues, Many thanks for your comments, which show how our community sees the problem. The discussion is obviously not finished yet. Let us actually try to say what is the MAIN problem with this article. The main problem is the picture of category theory it draws! Many of you give courses in category theory at various levels - beautiful courses showing that category theory provides a new most advanced level of thinking in mathematics ("thinking categorically!"), and has made major contributions to the unity of mathematics. So, why don't you compare the plan of your own course with this article? Surely you do not begin your course with resolutions of modules and you do not end it with "extended TQFT", do you? On the other hand there is clearly a desire to have a good content and context for category theory on wikipedia, which is often the first port of call for students, and those potentially interested, and so there are calls for an improved Timeline for category theory. To take in the whole subject in one timeline, with references, would seem an enormous and controversial task. We therefore propose that the present article be replaced by a list of topics with links to articles on timelines of those topics. And then each "timeline" should be written by a chosen group of experts. Our first draft of topics would be: 1. General category theory, including motivation 2. Abelian categories and homological algebra 3. Categories and groupoids in homotopical algebra and algebraic =20 topology 4. Topos theory 5. Monoidal, enriched, and higher-dimensional categories 6. Categorical algebra 7. Categorical topology 8. Categorical logic and foundation of mathematics 10. Categories in algebraic geometry 11. Categories in computer science 12. Categories in Physics There will be intersections of course, but we presume that is fine. As examples of timelines in other subjects, and their styles, see for example http://en.wikipedia.org/wiki/List_of_timelines#Science particularly those on Physics. We look forward to reactions to this proposal. Ronnie Brown George Janelidze [For admin and other information see: http://www.mta.ca/~cat-dist/ ]