From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6511 Path: news.gmane.org!not-for-mail From: John Stell Newsgroups: gmane.science.mathematics.categories Subject: RE: categories with several compositions? Date: Wed, 2 Feb 2011 16:11:26 +0000 Message-ID: References: Reply-To: John Stell NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1296693233 6749 80.91.229.12 (3 Feb 2011 00:33:53 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 3 Feb 2011 00:33:53 +0000 (UTC) Cc: "'categories@mta.ca'" To: "'Prof. Peter Johnstone'" Original-X-From: majordomo@mlist.mta.ca Thu Feb 03 01:33:45 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 1Pkn8q-0003hy-2s for gsmc-categories@m.gmane.org; Thu, 03 Feb 2011 01:33:44 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:51804) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Pkn8g-0005qh-MA; Wed, 02 Feb 2011 20:33:34 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Pkn8d-0000Wc-Ip for categories-list@mlist.mta.ca; Wed, 02 Feb 2011 20:33:31 -0400 Thread-Topic: categories: categories with several compositions? Thread-Index: AcvC7F3WnB4DxspjQgyqxwPQ5luFyAABwn8Q In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6511 Archived-At: Thanks for pointing that out. I should have been asking for each composition to have its own identity John=20 -----Original Message----- From: Prof. Peter Johnstone [mailto:P.T.Johnstone@dpmms.cam.ac.uk]=20 Sent: 02 February 2011 15:18 To: John Stell Cc: 'categories@mta.ca' Subject: Re: categories: categories with several compositions? 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 =3D x *i (y *j z) for all i,j > Substituting the common identity for y in this equation yields x *j z =3D 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/ ]