From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6016 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Eckmann-Hilton (Was: Tensor of monads) Date: Sat, 31 Jul 2010 13:34:26 -0700 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1280613520 2341 80.91.229.12 (31 Jul 2010 21:58:40 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 31 Jul 2010 21:58:40 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Jul 31 23:58:36 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 1OfK4f-00031C-Tv for gsmc-categories@m.gmane.org; Sat, 31 Jul 2010 23:58:34 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46606) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OfK3m-0002Rh-KC; Sat, 31 Jul 2010 18:57:38 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OfK3k-00021Z-9p for categories-list@mlist.mta.ca; Sat, 31 Jul 2010 18:57:36 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6016 Archived-At: Sergey Goncharov wrote in part: >But I guess, Eckmann-Hilton argument does not apply to >your previous example because it presupposes that the monoidal >structures share the unit, which was not the case there, was it? Actually, the requirements for Eckmann-Hilton are surprsingly weak! As long as you have two binary operations on a given set, each with its own unit, where one is a homomorphism WRT the other, then everything else (associativity, same unit, etc) follows. See http://ncatlab.org/nlab/show/Eckmann-Hilton+argument for details. --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]