From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6081 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: Re: Makkai's suggestion Date: Tue, 31 Aug 2010 01:01:52 +0000 Message-ID: References: Reply-To: David Leduc 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 1283299306 7053 80.91.229.12 (1 Sep 2010 00:01:46 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 1 Sep 2010 00:01:46 +0000 (UTC) Cc: categories To: John Baez Original-X-From: majordomo@mlist.mta.ca Wed Sep 01 02:01:45 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Oqals-0005ir-Aa for gsmc-categories@m.gmane.org; Wed, 01 Sep 2010 02:01:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49228) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OqakC-00066H-Bk; Tue, 31 Aug 2010 21:00:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Oqak7-0004lN-SH for categories-list@mlist.mta.ca; Tue, 31 Aug 2010 20:59:56 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6081 Archived-At: John Baez wrote: > Yes: most or all of the successful approaches to infinity-categories foll= ow > a philosophy of this general sort. =A0You can find a lot of references he= re: > > http://ncatlab.org/johnbaez/show/Towards+Higher+Categories Thank you for the reference. But I don't know where to start. Each author seems to be working with his own favorite special case of infinity-categories: (inf,1)-categories, opetopic and multitopic categories, simple omega-categories, theta-categories, protocategories... and so on. Is there a definitive definition of omega-categories somewhere in the literature or is it still unknown? Can it be stated in elementary terms (i mean in terms of object, arrows, ... without references to simplicial sets or topology) ? In the definition of a bicategory, one could replace the coherence axioms by the statement that all diagrams built from the canonical ismorphisms commute. Can it be generalized to n=3D3, ... , omega. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]