From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6388 Path: news.gmane.org!not-for-mail From: Nick Gurski Newsgroups: gmane.science.mathematics.categories Subject: Re: Bilimit question Date: Tue, 23 Nov 2010 13:04:13 +0000 Message-ID: References: Reply-To: Nick Gurski 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 1290558060 18517 80.91.229.12 (24 Nov 2010 00:21:00 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 24 Nov 2010 00:21:00 +0000 (UTC) Cc: categories To: Alex Hoffnung Original-X-From: majordomo@mlist.mta.ca Wed Nov 24 01:20:56 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 1PL36V-0005ta-JY for gsmc-categories@m.gmane.org; Wed, 24 Nov 2010 01:20:55 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:34784) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PL35k-000207-Jh; Tue, 23 Nov 2010 20:20:08 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PL35g-0008RK-4s for categories-list@mlist.mta.ca; Tue, 23 Nov 2010 20:20:04 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6388 Archived-At: Alex- The reference you are looking for is Cartesian Bicategories II by Carboni, Kelly, Walters, and Wood. Here is a link to the .pdf on the TAC homepage. http://www.tac.mta.ca/tac/volumes/19/6/19-06.pdf Nick Alex Hoffnung said the following on 23/11/2010 00:44: > Dear List, > > The weakest form of limits in a bicategory are defined by equivalences of > hom-categories in place of the slightly more strict version defined by > isomorphisms. Then the process of defining a monoidal structure on a > bicategory with finite products takes on a slightly different flavor in each > case. > > In the weak case, given a pair of 1-cells one must *choose* a monoidal > product, whereas in the latter case, a *unique choice* of monoidal product > can be obtained from the one-dimensional aspect of the universal property. > > I would guess that in the former case, one should not worry too much about > how to choose the product 1-cells, since the universal property will come to > the rescue when checking that one has indeed defined a monoidal structure on > the bicategory. > > Does anyone know of a reference which proves something along these lines? > > Best, > Alex > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]