From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5397 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: additions Date: Mon, 21 Dec 2009 14:20:11 -0500 (EST) Message-ID: References: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1261442607 12491 80.91.229.12 (22 Dec 2009 00:43:27 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 22 Dec 2009 00:43:27 +0000 (UTC) To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= , categories@mta.ca Original-X-From: categories@mta.ca Tue Dec 22 01:43:20 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NMsqN-00076n-VD for gsmc-categories@m.gmane.org; Tue, 22 Dec 2009 01:43:20 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NMsQp-0006Sw-Ib for categories-list@mta.ca; Mon, 21 Dec 2009 20:16:55 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5397 Archived-At: I would add something between 2 and 3 about Triples (allright,=20 monads) and Equational theories. Here is an example of the sort of thing we are up against. A colleague=20 called me this morning because a student had taken a set of notes (in=20 French) on his course and was interested in publishing it. My colleague=20 had an objection because in describing conformal isomorphism from the=20 complex plane (or maybe sphere) to itself, the student had used the word=20 "towards" (vers) instead of "on". His objection was that a conformal=20 isomorphism was something between two spaces, not from one to the other.=20 My answer was a specific such map was a map from one to the other. His=20 reply essentially was, "Oh, it's category theory language. Well, I won't= =20 allow any of that in MY notes. No analyst would use that language." Michael On Mon, 21 Dec 2009, Joyal, Andr=E9 wrote: > In my message to John Baez, I wrote: > >> I can distinguish approximatly 6 major currents: > >> 1) Algebraic topology and homological algebra >> 2) Abelian categories >> 3) Algebraic Geometry and topos theory >> 4) Logic and elementary topos theory >> 5) Category theory and computer science >> 6) Higher categories with homotopy theory > > The list is too restrictive. I would like to expand it further: > > 1) Algebraic topology and homological algebra > 2) Abelian categories > 3) Algebraic geometry and topos theory > 4) General cartesian algebra > 5) Categorical logic > 6) Homotopical algebra > 7) Elementary topos theory and set theory > 8) Monoidal categories and enriched category theory > 9) General tensor algebra and coalgebra > 10) Category theory and computer science > 11) Quantum field theory > 12) Higher categories and homotopy theory > > Algebraic theories and limit sketches are included in (4). > Multicategories, operads are included in (9). > > I have included Quillen homotopical algebra in (6). > > Best, > Andr=E9 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]