From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7170 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: Good identity Date: Thu, 26 Jan 2012 14:00:09 -0500 Message-ID: Reply-To: David Leduc NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1327700123 26553 80.91.229.12 (27 Jan 2012 21:35:23 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 27 Jan 2012 21:35:23 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Fri Jan 27 22:35:19 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RqtS2-00031T-Vj for gsmc-categories@m.gmane.org; Fri, 27 Jan 2012 22:35:19 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:35329) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RqtRE-000066-HF; Fri, 27 Jan 2012 17:34:28 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RqtRF-0008My-4l for categories-list@mlist.mta.ca; Fri, 27 Jan 2012 17:34:29 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7170 Archived-At: 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/ ]