From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5392 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Sun, 20 Dec 2009 12:50:21 -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 1261356787 24216 80.91.229.12 (21 Dec 2009 00:53:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 21 Dec 2009 00:53:07 +0000 (UTC) To: "John Baez" , Original-X-From: categories@mta.ca Mon Dec 21 01:53:00 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 1NMWWB-0003Jv-Vq for gsmc-categories@m.gmane.org; Mon, 21 Dec 2009 01:53:00 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NMW5D-0002qh-AK for categories-list@mta.ca; Sun, 20 Dec 2009 20:25:07 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5392 Archived-At: 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/ ]