From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5847 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: lax V-functors Date: Mon, 24 May 2010 14:09:29 -0400 Message-ID: References: Reply-To: Michael Shulman 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 1274809728 6193 80.91.229.12 (25 May 2010 17:48:48 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 25 May 2010 17:48:48 +0000 (UTC) Cc: categories@mta.ca To: =?ISO-8859-1?Q?Bj=F6rn_Gohla?= Original-X-From: categories@mta.ca Tue May 25 19:48:47 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OGyFB-0007jG-QZ for gsmc-categories@m.gmane.org; Tue, 25 May 2010 19:48:46 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OGy0A-0003UH-5T for categories-list@mta.ca; Tue, 25 May 2010 14:33:14 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5847 Archived-At: Dear Bj=F6rn, In my recent preprint "Not every pseudoalgebra is equivalent to a strict one" (arXiv:1005.1520), I had occasion to consider pseudo V-categories, pseudo V-functors, and V-icons for such a V -- these form the 2-category Ps-T-Alg for a suitable 2-monad on the 2-category of V-enriched graphs. Obviously lax T-morphisms will similarly be lax V-functors. I didn't have any need for general V-transformations or modifications, and they don't fall as naturally out of the 2-monad setup, but I agree that the definitions are easy to write down. I would also be interested to hear who may have studied these notions in general. Best, Mike 2010/5/24 Bj=F6rn Gohla : > dear cocategorists, > > given a monoidal 2-category V (i.e. \tensor is a 2-functor in each variab= le) > there is an obvious definition of lax V-functors, lax V-transformations a= nd > modifications between V-categories (in the ordinary sense). has this been > studied anywhere? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]