From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5356 Path: news.gmane.org!not-for-mail From: Matias del Hoyo Newsgroups: gmane.science.mathematics.categories Subject: question concerning lax functors Date: Sat, 12 Dec 2009 18:19:40 -0300 Message-ID: Reply-To: Matias del Hoyo NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1260746117 7049 80.91.229.12 (13 Dec 2009 23:15:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 13 Dec 2009 23:15:17 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Mon Dec 14 00:15:10 2009 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 4.50) id 1NJxeg-0000hp-Bs for gsmc-categories@m.gmane.org; Mon, 14 Dec 2009 00:15:10 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NJx7f-0004GE-Go for categories-list@mta.ca; Sun, 13 Dec 2009 18:41:03 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5356 Archived-At: Hi, I'm Matias del Hoyo from Buenos Aires and I wonder if someone could help me by giving some reference about the following. If 2Cat is the category of (strict) 2-categories and (strict) 2-functors, and Lax is the category of (strict) 2-categories and (normal) lax functors, then I guess that the inclusion 2cat --> Lax admits a left adjoint, namely for a 2-category C there is another FC and a lax functor i:C --> FC such that for every lax functor v:C --> D there exists a unique 2-functor u:FC --> D satisfying v=ui. In my thesis I constructed FC in the case C is a category (2-category with trivial 2-cells) by using subdivision of small categories. This was enough for my purpose (a version of Quillen's Thm A for lax functors), but the general case might be of interest and it should be well known. Thanks in advance! Matias del Hoyo [For admin and other information see: http://www.mta.ca/~cat-dist/ ]