From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6405 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: double 2-categories Date: Tue, 07 Dec 2010 14:13:25 +0000 Message-ID: References: Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1291776047 29812 80.91.229.12 (8 Dec 2010 02:40:47 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 8 Dec 2010 02:40:47 +0000 (UTC) Cc: categories@mta.ca To: Ondrej Rypacek Original-X-From: majordomo@mlist.mta.ca Wed Dec 08 03:40:42 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PQ9xS-0007Sn-Fh for gsmc-categories@m.gmane.org; Wed, 08 Dec 2010 03:40:42 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:46536) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PQ9wt-0006fV-Q5; Tue, 07 Dec 2010 22:40:07 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PQ9wp-0006f3-VO for categories-list@mlist.mta.ca; Tue, 07 Dec 2010 22:40:04 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6405 Archived-At: I am not sure why there is the restriction to having 2-categories as edge arrows. They could be double categories, perhaps. Would this then be any more general than a 4-fold category? A definition of n-fold category is given in 34. (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 371-386. and this also contains a definition of what was later called a globular set, giving a notion of what we now call a strict globular n-category, though the emphasis in the paper is on the groupoid case. Ronnie On 07/12/2010 12:59, Ondrej Rypacek wrote: > Dear all, > > Is there a standard reference for what could be called a double-2-category, > by which I mean a double category where the categories of horizontal and > vertical arrows are 2-categories ? > It would be a special case of a "triple category", I guess, where > there are objects, arrows in three directions, cells for each distinct > pair of the directions, and cubes surrounded by cells. > > > Many thanks, > Ondrej > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]