From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7172 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: Re: Good identity Date: Fri, 27 Jan 2012 21:11:54 -0500 Message-ID: References: Reply-To: David Leduc NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1327780049 11827 80.91.229.3 (28 Jan 2012 19:47:29 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 28 Jan 2012 19:47:29 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Sat Jan 28 20:47:28 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RrEFA-0005ru-C9 for gsmc-categories@m.gmane.org; Sat, 28 Jan 2012 20:47:24 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:36893) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RrEDk-0007W8-PI; Sat, 28 Jan 2012 15:45:56 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RrEDl-00050Z-4R for categories-list@mlist.mta.ca; Sat, 28 Jan 2012 15:45:57 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7172 Archived-At: OK, I found it by myself. I was confused and I could not see the obvious. For reference, I just have to take the component at (H,G,F) of the associativity constraint (a natural isomorphism) of the bicategory. On 1/26/12, David Leduc wrote: > Hi, > > Let F, G, and H be composable functors. I can define the canonical > natural transformation from (H o G) o F to H o (G o F) without relying > on the evil fact that (H o G) o F = H o (G o F). I just define it > componentwisely: for each X, I take id_(H(G(F(X)))). > > This works in the bicategory of small categories. But now if F, G and > H are 1-cells in any bicategory, how can I define the canonical 2-cell > from (H o G) o F to H o (G o F) without relying on the evil fact that > (H o G) o F = H o (G o F). > > Thanks! > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]