From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6692 Path: news.gmane.org!not-for-mail From: Finn Lawler Newsgroups: gmane.science.mathematics.categories Subject: Re: Gray tensor product Date: Fri, 27 May 2011 18:16:58 +0100 Message-ID: Reply-To: Finn Lawler NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1306525282 24479 80.91.229.12 (27 May 2011 19:41:22 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 27 May 2011 19:41:22 +0000 (UTC) Cc: categories@mta.ca To: Mike Stay Original-X-From: majordomo@mlist.mta.ca Fri May 27 21:41:17 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 1QQ2uL-0005Ff-9l for gsmc-categories@m.gmane.org; Fri, 27 May 2011 21:41:17 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:35050) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QQ2rd-0000aQ-A8; Fri, 27 May 2011 16:38:29 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QQ2rb-0003rN-04 for categories-list@mlist.mta.ca; Fri, 27 May 2011 16:38:27 -0300 Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6692 Archived-At: Mike Stay wrote: > Has anyone "unpacked" the meaning of the Gray tensor product of strict > 2-categories? I'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 (Springer LNM 391) is the original reference. Theorem 4.9 constructs the 'lax' tensor product. A good reference for the 'pseudo' tensor product is chapter 5 of Nick Gurski's 2007 Ph.D. thesis 'An algebraic theory of tricategories'. FL -- Finn Lawler [For admin and other information see: http://www.mta.ca/~cat-dist/ ]