From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6510 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: categories with several compositions? Date: Wed, 2 Feb 2011 15:17:42 +0000 (GMT) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1296693164 6514 80.91.229.12 (3 Feb 2011 00:32:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 3 Feb 2011 00:32:44 +0000 (UTC) Cc: "'categories@mta.ca'" To: John Stell Original-X-From: majordomo@mlist.mta.ca Thu Feb 03 01:32:40 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Pkn7l-0003G4-69 for gsmc-categories@m.gmane.org; Thu, 03 Feb 2011 01:32:37 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:51798) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Pkn7S-0005lo-FR; Wed, 02 Feb 2011 20:32:18 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Pkn7Q-0000VY-24 for categories-list@mlist.mta.ca; Wed, 02 Feb 2011 20:32:16 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6510 Archived-At: On Wed, 2 Feb 2011, John Stell wrote: > > Can anyone tell me whether these structures have been studied anywhere? > > A kind of generalized monoid with two or more compositions *1, *2, etc > with a single identity that works for both and where > (x *i y) *j z = x *i (y *j z) for all i,j > Substituting the common identity for y in this equation yields x *j z = x *i z, so the compositions all coincide. Similarly in the multiple-object case. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]