From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7371 Path: news.gmane.org!not-for-mail From: Mark Weber Newsgroups: gmane.science.mathematics.categories Subject: Re: Alternative closed structure on Cat Date: Fri, 6 Jul 2012 09:42:09 +1000 Message-ID: References: Reply-To: Mark Weber NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1278) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1341578426 10405 80.91.229.3 (6 Jul 2012 12:40:26 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 6 Jul 2012 12:40:26 +0000 (UTC) Cc: ondrej.rypacek@gmail.com, categories@mta.ca (Categories List) To: selinger@mathstat.dal.ca (Peter Selinger) Original-X-From: majordomo@mlist.mta.ca Fri Jul 06 14:40:26 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Sn7pb-0006EV-Cu for gsmc-categories@m.gmane.org; Fri, 06 Jul 2012 14:40:20 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:54329) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Sn7pD-0006Ve-Gu; Fri, 06 Jul 2012 09:39:55 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Sn7pD-0004rg-CV for categories-list@mlist.mta.ca; Fri, 06 Jul 2012 09:39:55 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7371 Archived-At: Dear Ondrej and Peter The fact to which Peter referred, that the tensor product in question > is the unique other symmetric monoidal closed > structure on Cat was proved in the paper [1] F. Foltz, G.M.Kelly, and C. Lair, "Algebraic categories with few = biclosed monoidal structures or none", JPAA 17:171-177, 1980 As for the name, this tensor product has been called the "funny tensor = product" by some authors. But as I argued in my paper [2] Free products of higher operad algebras http://arxiv.org/abs/0909.4722 in which such a tensor product is defined for any structure definable by = a "normalised higher operad" in the sense of Batanin, the name "free = product" is a better choice of terminology. Mark Weber= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]