From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7374 Path: news.gmane.org!not-for-mail From: =?ISO-8859-1?Q?Omar_Antol=EDn_Camarena?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Alternative closed structure on Cat Date: Fri, 6 Jul 2012 09:03:26 -0400 Message-ID: References: Reply-To: =?ISO-8859-1?Q?Omar_Antol=EDn_Camarena?= NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1341675650 25073 80.91.229.3 (7 Jul 2012 15:40:50 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 7 Jul 2012 15:40:50 +0000 (UTC) Cc: Categories List To: Ondrej Rypacek Original-X-From: majordomo@mlist.mta.ca Sat Jul 07 17:40:48 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 1SnX7k-00034j-1c for gsmc-categories@m.gmane.org; Sat, 07 Jul 2012 17:40:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:54644) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SnX6n-0003Is-5M; Sat, 07 Jul 2012 12:39:45 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SnX6n-0000aE-JR for categories-list@mlist.mta.ca; Sat, 07 Jul 2012 12:39:45 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7374 Archived-At: Isn't this funny tensor product of C and D the pushout of the inclusions of (Ob C x Ob D) into (C x Ob D) and (Ob C x D) --where Ob C is the discrete category with the same objects as C? On Fri, Jul 6, 2012 at 5:13 AM, Ondrej Rypacek w= rote: > Thanks for all answers and references. It's much appreciated! > > Before I tuck in, am I likely to find a definition in terms of a colimit? > > Ondrej > > > > On 6 Jul 2012, at 00:42, Mark Weber wrote: > >> 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 bic= losed monoidal structures or none", JPAA 17:171-177, 1980 >> >> As for the name, this tensor product has been called the "funny tensor p= roduct" 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 produ= ct" is a better choice of terminology. >> >> Mark Weber > > --=20 Omar Antol=EDn Camarena [For admin and other information see: http://www.mta.ca/~cat-dist/ ]