From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6387 Path: news.gmane.org!not-for-mail From: Alex Hoffnung Newsgroups: gmane.science.mathematics.categories Subject: Bilimit question Date: Mon, 22 Nov 2010 19:44:49 -0500 Message-ID: Reply-To: Alex Hoffnung NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1290514029 29799 80.91.229.12 (23 Nov 2010 12:07:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 23 Nov 2010 12:07:09 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Tue Nov 23 13:07:05 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 1PKreI-0002Ka-NO for gsmc-categories@m.gmane.org; Tue, 23 Nov 2010 13:07:02 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:38064) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PKrdj-0004e8-T2; Tue, 23 Nov 2010 08:06:27 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PKrdg-00080V-5V for categories-list@mlist.mta.ca; Tue, 23 Nov 2010 08:06:24 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6387 Archived-At: 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/ ]