From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6693 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Re: Gray tensor product Date: Fri, 27 May 2011 14:37:38 -0700 Message-ID: References: Reply-To: Mike Stay NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1306566610 15881 80.91.229.12 (28 May 2011 07:10:10 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 28 May 2011 07:10:10 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Sat May 28 09:10:04 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QQDer-0001fK-7R for gsmc-categories@m.gmane.org; Sat, 28 May 2011 09:10:01 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45225) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QQDcl-0004ij-52; Sat, 28 May 2011 04:07:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QQDcc-00063N-GE for categories-list@mlist.mta.ca; Sat, 28 May 2011 04:07:43 -0300 In-Reply-To: <20110527171658.GA2358@sappho> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6693 Archived-At: On Fri, May 27, 2011 at 10:16 AM, Finn Lawler wrote: > Mike Stay wrote: >> Has anyone "unpacked" the meaning of the Gray tensor product of strict >> 2-categories? =A0I'm looking for something like "the Gray product C >> tensor D is the 2-category whose >> - objects are pairs (c,d) >> - morphisms are ... >> - 2-morphisms are ..." > > Gray's book Formal Category Theory: Adjointness for 2-Categories (Springe= r LNM 391) is the original reference. =A0Theorem 4.9 constructs the 'lax' t= ensor product. =A0A good reference for the 'pseudo' tensor product is chapt= er 5 of Nick Gurski's 2007 Ph.D. thesis 'An algebraic theory of tricategori= es'. Thanks to everyone! Gurski's exposition is exactly what I was looking for. --=20 Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]