From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1552 Path: news.gmane.org!not-for-mail From: Claudio Hermida Newsgroups: gmane.science.mathematics.categories Subject: Re: Adjoints in bicategories Date: Fri, 23 Jun 2000 16:13:56 +0000 Organization: CMA, IST Message-ID: <39538CC4.CEB0D163@math.ist.utl.pt> References: <20000622124507.EF71C451D@mail.cs.uu.nl> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017918 31754 80.91.229.2 (29 Apr 2009 15:11:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:11:58 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Jun 23 14:40:12 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id OAA18986 for categories-list; Fri, 23 Jun 2000 14:35:01 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Mozilla 4.7 [en] (X11; I; Linux 2.2.12-20 i686) X-Accept-Language: en Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:1552 Archived-At: Frank Atanassow wrote: > I'm looking for definitions of (the weak 2-dimensional analogues of 1-) > products and coproducts for bicategories, and also adjoints. In his 1967 > article "Introduction to Bicategories, Part I" Benabou promises to treat > biadjoints in a sequel, but I gather this was never published. Gray treats a > notion of "quasi-adjointness" in "Formal Category Theory"; is this accepted as > the "right" generalization? > > Pointers to definitions of these concepts in one of the approaches to weak > n-categories would be welcome as well. Relevant references: Kelly, G. M. Elementary observations on $2$-categorical limits. Bull. Austral. Math. Soc. 39 (1989), no. 2, 301--317. Power, A. J. Coherence for bicategories with finite bilimits. I. Categories in computer science and logic (Boulder, CO, 1987),341--347, Contemp. Math., 92, Amer. Math. Soc., Providence, RI, 1989. Betti, Renato; Power, A. John On local adjointness of distributive bicategories. Boll. Un. Mat. Ital. B (7) 2 (1988), no. 4, 931--947. Bird, G. J.; Kelly, G. M.; Power, A. J.; Street, R. H. Flexible limits for $2$-categories. J. Pure Appl. Algebra 61 (1989), no. 1, 1--27.