From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5613 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: Composing modifications Date: Thu, 4 Mar 2010 16:25:00 -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 1267831062 14340 80.91.229.12 (5 Mar 2010 23:17:42 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 5 Mar 2010 23:17:42 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Sat Mar 06 00:17:38 2010 connect(): Connection refused 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 1Nngm2-00052F-4e for gsmc-categories@m.gmane.org; Sat, 06 Mar 2010 00:17:38 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NngFV-0006b2-Fv for categories-list@mta.ca; Fri, 05 Mar 2010 18:44:01 -0400 In-Reply-To: <4B8F6048.7000903@btinternet.com> Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5613 Archived-At: Ronnie Brown wrote; Has anyone formulated a cubical (square?) version of bicategory or higher? > Dominic Verity invented "double bicategories", which are the fully weakened version of double categories. Unfortunately, his thesis can only be obtained by special shipment from Australia. Someday someone will scan it and make it more widely available! Luckily, you can see the definition in this paper: Jeffrey Morton Double bicategories and double cospans http://arxiv.org/abs/math/0611930 For higher dimensions, try: Marco Grandis HIGHER COSPANS AND WEAK CUBICAL CATEGORIES (COSPANS IN ALGEBRAIC TOPOLOGY, I) http://tac.mta.ca/tac/volumes/18/12/18-12abs.html and also parts II and III of this series. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]