From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4499 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: biadjoint biequivalences and spans in 2-categories Date: Wed, 20 Aug 2008 07:56:44 +0100 (BST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019984 13588 80.91.229.2 (29 Apr 2009 15:46:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:24 +0000 (UTC) To: categories Original-X-From: rrosebru@mta.ca Wed Aug 20 08:22:35 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 20 Aug 2008 08:22:35 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KVll6-0001Px-Av for categories-list@mta.ca; Wed, 20 Aug 2008 08:21:48 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 34 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:4499 Archived-At: > At the beginning of section 3 he defines a bicategory of spans from A to > B in any bicategory, and given finite bilimits, essentially describes > how to construct what one might call an "unbiased tricategory" of spans > (of course, the definition of tricategory didn't exist at the time). > > He doesn't give any details of the proofs, but one could probably > construct a detailed proof from these ideas without much more than > tedium. I don't know whether anyone has written them out. One amusing thing about the tricategory of spans in a 2-category, with composition by iso-comma object, is that it is barely a tricategory. Binary composition is associative up to iso; it is only the unitality which is really up to equivalence. Something similar happens if you define a tricategory of biprofunctors. Richard