From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5819 Path: news.gmane.org!not-for-mail From: Newsgroups: gmane.science.mathematics.categories Subject: Re: The stabilisation theorem Date: Mon, 17 May 2010 23:27:45 -0400 Message-ID: References: Reply-To: 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: dough.gmane.org 1274225523 11918 80.91.229.12 (18 May 2010 23:32:03 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 18 May 2010 23:32:03 +0000 (UTC) To: "John Baez" , "categories" Original-X-From: categories@mta.ca Wed May 19 01:32:02 2010 connect(): No such file or directory 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 4.69) (envelope-from ) id 1OEWGX-0005TH-QK for gsmc-categories@m.gmane.org; Wed, 19 May 2010 01:32:01 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OEVl2-0007AM-4N for categories-list@mta.ca; Tue, 18 May 2010 19:59:28 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5819 Archived-At: Dear John, > It seems all the hard work is packed into the formalism that > underlies the proof. I cannot resist describing a key idea of my proof. It is to construct categories from homotopy types rather than from sets. The notion of category is homotopy essentially algebraic: "A category is essentially the same thing as a complete Segal object X satisfying an extra condition:=20 the (source, target) map X_1-->X_0 times X_0=20 is a 0-cover (a map is a 0-cover if its homotopy fibers are discrete). This is like constructing the "natural" (or folk") model structure on Cat from a model structure on simplicial diagrams of spaces (spaces =3D simplical sets). A similar description applies to (weak) n-categories. The Stabilisation Hypothesis was a great conjecture. Let me congratulate you and Jim Dolan for formulating it. Best, Andr=E9 -------- Message d'origine-------- De: categories@mta.ca de la part de John Baez Date: dim. 16/05/2010 14:44 =C0: categories Objet : categories: Re: The stabilisation theorem =20 Andr=E9 wrote: Too simple to be true? > No, I always hoped for a simple proof! And this proof is not "too simple". It seems all the hard work is packed into the formalism that underlies the proof. And that's how it should be, I think. So, I'm happy. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]