From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6079 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: Makkai's suggestion Date: Mon, 30 Aug 2010 12:53:17 +0800 Message-ID: References: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1283185774 16836 80.91.229.12 (30 Aug 2010 16:29:34 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 30 Aug 2010 16:29:34 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Mon Aug 30 18:29:30 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Oq7Eg-0007uT-8t for gsmc-categories@m.gmane.org; Mon, 30 Aug 2010 18:29:30 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:33685) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Oq7Cj-0006zi-P1; Mon, 30 Aug 2010 13:27:29 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Oq7Cg-0001fQ-Ne for categories-list@mlist.mta.ca; Mon, 30 Aug 2010 13:27:26 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6079 Archived-At: David Leduc wrote: In "Towards a categorical foundation of mathematics", Makkai wrote that: > > "This suggests that, possibly, the right approach to the definition of weak > n-category is to aim at formulating all coherence conditions at once, > regardless the fact that this might give a very "theoretical" definition. > It > would then be a separate, and still very important, project to find a > (hopefully) finite and concise set of coherence conditions that would be > enough to imply all coherence conditions." > > It was 15 years ago! Did this approach give something? > Yes: most or all of the successful approaches to infinity-categories follow a philosophy of this general sort. You can find a lot of references here: http://ncatlab.org/johnbaez/show/Towards+Higher+Categories Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]