From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6285 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: horizontal composition in a 2-category Date: Mon, 4 Oct 2010 12:42:43 +0000 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 1286280833 9395 80.91.229.12 (5 Oct 2010 12:13:53 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 5 Oct 2010 12:13:53 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Tue Oct 05 14:13:51 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 1P36P0-0008SW-Ni for gsmc-categories@m.gmane.org; Tue, 05 Oct 2010 14:13:50 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41995) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P36Nr-0001IU-9z; Tue, 05 Oct 2010 09:12:39 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P36Nl-0000C6-W9 for categories-list@mlist.mta.ca; Tue, 05 Oct 2010 09:12:34 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6285 Archived-At: Hi, A 2-category C is a category enriched over Cat. This gives me two compositions. * The functor C(Y,Z) x C(X,Y) -> C(X,Z) * and for each X and Y in C the function (C(X,Y))(g,h) x (C(X,Y))(f,g) -> (C(X,Y))(f,h) But how can I derive the horizontal composition: (C(Y,Z))(g1,g2) x (C(X,Y))(f1,f2) -> (C(X,Z))(g1 o f1, g2 o f2) = ??? I the case of the 2-category of categories, I know how to define horizontal composition (Godement product) in a pointwise manner, but how does it generalize to 2-categories? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]