From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5394 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: additions Date: Mon, 21 Dec 2009 03:43:17 -0500 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1261405017 12502 80.91.229.12 (21 Dec 2009 14:16:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 21 Dec 2009 14:16:57 +0000 (UTC) To: Original-X-From: categories@mta.ca Mon Dec 21 15:16:50 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 1NMj45-0007PV-MC for gsmc-categories@m.gmane.org; Mon, 21 Dec 2009 15:16:49 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NMiUz-0000Gb-AS for categories-list@mta.ca; Mon, 21 Dec 2009 09:40:33 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5394 Archived-At: 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=20 >4) Logic and elementary topos theory >5) Category theory and computer science >6) Higher categories with homotopy theory =20 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=20 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 =20 Algebraic theories and limit sketches are included in (4). Multicategories, operads are included in (9). I have included Quillen homotopical algebra in (6). Best,=20 Andr=E9 -------- Message d'origine-------- De: categories@mta.ca de la part de Joyal, Andr=E9 Date: dim. 20/12/2009 12:50 =C0: John Baez; categories@mta.ca Objet : categories: Re: A well kept secret? =20 John Baez wrote: >They fought to convince the world that category theory was >worthwhile. Some feel they lost that fight. We came along later and >are a bit puzzled by that attitude: if you look around at the >landscape of mathematics today, categories are everywhere! From >Grothendieck to Voevodsky to Lurie, etc., much of the most exciting >mathematics of our era would be inconceivable without categories. Like most fields of mathematics, category theory keeps growing and = evolving.=20 It may be hard to identify the mechanism of this evolution=20 but fashion must be playing a role. But why are certain subjects becoming hot at a given time? Probably because they resonate with new developments outside category = theory. When a trend becomes hot, it gives rise to a permanent current.=20 I was able to distinguish approximatly 6 major currents: 1) Algebraic topology and homological algebra 2) Abelian categories 3) Algebraic Geometry and topos theory=20 4) Logic and elementary topos theory 5) Category theory and computer science 6) Higher categories with homotopy theory =20 Here is an example of a recent applications of category theory to = geometry: "Associahedral categories, particles and Morse functor"=20 by Jean-Yves Welschinger http://arxiv.org/abs/0906.4712=20 The n-category caff=E9 is an extraordinary experiment in=20 research collaboration and dissimination of knowledge. It maybe the way of the future. But an old mathematicians like me find it=20 difficult to adapt to this new form of collaboration.=20 >The only real question is whether our current civilization, based on = burning >carbon, tearing up forests, and destroying oceans, lasts long enough to = see >this change. Yep! And we should not remain passive. Best, AJ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]