From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6508 Path: news.gmane.org!not-for-mail From: John Stell Newsgroups: gmane.science.mathematics.categories Subject: categories with several compositions? Date: Wed, 2 Feb 2011 09:58:43 +0000 Message-ID: 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 1296656083 28276 80.91.229.12 (2 Feb 2011 14:14:43 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 2 Feb 2011 14:14:43 +0000 (UTC) To: "'categories@mta.ca'" Original-X-From: majordomo@mlist.mta.ca Wed Feb 02 15:14:38 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 1PkdTi-0000Wb-5I for gsmc-categories@m.gmane.org; Wed, 02 Feb 2011 15:14:38 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:50460) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PkdTZ-000211-0M; Wed, 02 Feb 2011 10:14:29 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PkdTT-0005tx-AB for categories-list@mlist.mta.ca; Wed, 02 Feb 2011 10:14:23 -0400 Accept-Language: en-US, en-GB Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6508 Archived-At: 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 More generally, a kind of category with several compositions: for each object y there is a set Dy and instead of the usual C(x,y) x C(y,z) -> C(x,z) we have Dy -> [C(x,y) x C(y,z), C(x,z)] So you have a family of compositions at each object which "associate with each other" in the manner of the above equation, and where there is a single identity for each object. thanks John Stell [For admin and other information see: http://www.mta.ca/~cat-dist/ ]