From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7373 Path: news.gmane.org!not-for-mail From: Ondrej Rypacek Newsgroups: gmane.science.mathematics.categories Subject: Re: Alternative closed structure on Cat Date: Fri, 6 Jul 2012 10:13:27 +0100 Message-ID: References: Reply-To: Ondrej Rypacek 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 1341578519 11141 80.91.229.3 (6 Jul 2012 12:41:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 6 Jul 2012 12:41:59 +0000 (UTC) To: Categories List Original-X-From: majordomo@mlist.mta.ca Fri Jul 06 14:41:59 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 1Sn7rB-0000e5-AB for gsmc-categories@m.gmane.org; Fri, 06 Jul 2012 14:41:57 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:54346) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Sn7qk-0006kU-B6; Fri, 06 Jul 2012 09:41:30 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Sn7qj-0004uH-UW for categories-list@mlist.mta.ca; Fri, 06 Jul 2012 09:41:29 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7373 Archived-At: 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?=20 Ondrej On 6 Jul 2012, at 00:42, Mark Weber wrote: > Dear Ondrej and Peter >=20 > The fact to which Peter referred, that the tensor product in question >=20 >> is the unique other symmetric monoidal closed >> structure on Cat >=20 > 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 >=20 > As for the name, this tensor product has been called the "funny tensor = product" by some authors. But as I argued in my paper >=20 > [2] Free products of higher operad algebras > http://arxiv.org/abs/0909.4722 >=20 > 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. >=20 > Mark Weber [For admin and other information see: http://www.mta.ca/~cat-dist/ ]