From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5030 Path: news.gmane.org!not-for-mail From: Tom Leinster Newsgroups: gmane.science.mathematics.categories Subject: Re: query Date: Fri, 26 Jun 2009 16:51:56 +0100 (BST) Message-ID: Reply-To: Tom Leinster NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII X-Trace: ger.gmane.org 1246089274 13655 80.91.229.12 (27 Jun 2009 07:54:34 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 27 Jun 2009 07:54:34 +0000 (UTC) To: jds@math.upenn.edu Original-X-From: categories@mta.ca Sat Jun 27 09:54:28 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MKSjw-0004tG-TD for gsmc-categories@m.gmane.org; Sat, 27 Jun 2009 09:54:25 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MKSGH-00028T-4o for categories-list@mta.ca; Sat, 27 Jun 2009 04:23:45 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5030 Archived-At: Dear Jim, On Wed, 24 Jun 2009, jim stasheff wrote: > Mac Lane coherence can be deduced from the simple connectivity of the > associahedron Surely that's not true, assuming that by "Mac Lane coherence" you mean Mac Lane's coherence theorem for monoidal categories. The associahedra (and in particular the pentagon) say nothing about the unit coherence isomorphisms, X \otimes I ----> X <---- I \otimes X. To make it true, surely you need to weaken Mac Lane's theorem to a statement about "semigroupal" categories, i.e. monoidal categories without unit...? Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]