From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6140 Path: news.gmane.org!not-for-mail From: Jocelyn Paine Newsgroups: gmane.science.mathematics.categories Subject: Re: Evil in bicategories Date: Sun, 12 Sep 2010 07:03:41 +0100 (BST) Message-ID: References: Reply-To: Jocelyn Paine NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1284320638 3165 80.91.229.12 (12 Sep 2010 19:43:58 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 12 Sep 2010 19:43:58 +0000 (UTC) Cc: categories To: David Leduc Original-X-From: majordomo@mlist.mta.ca Sun Sep 12 21:43:54 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OusSv-0003QD-UL for gsmc-categories@m.gmane.org; Sun, 12 Sep 2010 21:43:54 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:40042) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OusQp-0007bU-0u; Sun, 12 Sep 2010 16:41:43 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OusQm-0001pV-MP for categories-list@mlist.mta.ca; Sun, 12 Sep 2010 16:41:40 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6140 Archived-At: On Sat, 11 Sep 2010, David Leduc wrote: > In a bicategory, composition of 1-cells is associative up to > isomorphism. Because it would be evil to insist that h o (g o f) is > equal to (h o g) o f. However the source and target objects of those > compositions must be equal. Isn't it evil? Why not weaken this > requirement by saying that the sources (respectively, targets) of h o > (g o f) and (h o g) o f must only be isomorphic? > Your question made me wonder why the axioms for ordinary categories, i.e. 1-categories, insist that in composing f:A->B and g:C->D, B and C must be equal. Isn't it just as evil not to allow them to be merely isomorphic? Jocelyn Paine http://www.j-paine.org Jocelyn's Cartoons: http://www.j-paine.org/blog/jocelyns_cartoons/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]