From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5144 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Multi-allegories Date: Sun, 13 Sep 2009 13:48:31 -0700 Message-ID: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1252957327 22257 80.91.229.12 (14 Sep 2009 19:42:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 14 Sep 2009 19:42:07 +0000 (UTC) To: Categories list Original-X-From: categories@mta.ca Mon Sep 14 21:42:00 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 1MnHR1-00035z-8f for gsmc-categories@m.gmane.org; Mon, 14 Sep 2009 21:41:59 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MnGub-0004Xp-So for categories-list@mta.ca; Mon, 14 Sep 2009 16:08:29 -0300 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5144 Archived-At: Has anybody looked at a combination of allegories and multicategories that would capture (some of) the features of the algebra of relations of finite arity (not just binary) on sets? So we would have Mor(A_1,...,A_n) for any n = 0,1,2,..., each a meet semilattice with an involution for each pair of indices, and composition Mor(A_1,...,C,...,A_n) x Mor(B_1,...,C,...,B_m) to Mor (A_1,...,...,A_n,B_1,...,...,B_m) across any repeated object, satisfying some (hopefully) obvious conditions. Of course, for functions of even arbitrary finite arity, we only need Set as a good old cartesian monoidal category; I really am looking for something weak analogous to a multicategory. But if there's only material on monoidal or cartesian allegories, or something like that, then that would still be helpful. My motivations are entirely theoretical, so don't feel limited. There's also the matter of relations of infinite arity, but I'm not so much concerned about that right now. I would appreciate any pointers to literature, useful folk theorems, or even just the correct word to search on ("multiallegory" is no good). --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]