From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4502 Path: news.gmane.org!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Re: biadjoint biequivalences Date: Wed, 20 Aug 2008 21:39:59 +0930 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019986 13597 80.91.229.2 (29 Apr 2009 15:46:26 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:26 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Aug 21 09:36:33 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 21 Aug 2008 09:36:33 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KW9MO-0006nD-M0 for categories-list@mta.ca; Thu, 21 Aug 2008 09:33:52 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 37 Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:4502 Archived-At: Hi all, Tom Fiore wrote: > Theorem. 9.17 > Let X and A be strict 2-categories, and G:A -> X a pseudo functor. Ther= e > exists a left biadjoint for G if and only if for every object x of X th= ere > exists an object r of A and a biuniversal arrow x -> Gr from x to G. Of course this begs the obvious question, how hard is this to generalise = to bicategories? I'm surprised no-one has mentioned Gurksi's thesis, which I just came acr= oss. Appendix A has details of adjunctions in bicategories, and biadjunctions = in tricategories, citing Verity's thesis in the case of Gray-categories. Best, David