From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6907 Path: news.gmane.org!not-for-mail From: =?UTF-8?Q?Jonathan_CHICHE_=E9=BD=8A=E6=AD=A3=E8=88=AA?= Newsgroups: gmane.science.mathematics.categories Subject: Strictifying normal lax functors Date: Tue, 20 Sep 2011 11:10:37 +0200 Message-ID: Reply-To: =?UTF-8?Q?Jonathan_CHICHE_=E9=BD=8A=E6=AD=A3=E8=88=AA?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1316516635 8147 80.91.229.12 (20 Sep 2011 11:03:55 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 20 Sep 2011 11:03:55 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Tue Sep 20 13:03:51 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 1R5y7D-0007UX-Gq for gsmc-categories@m.gmane.org; Tue, 20 Sep 2011 13:03:51 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:39205) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R5y5e-0000JC-Fi; Tue, 20 Sep 2011 08:02:14 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R5y5c-0001xx-U2 for categories-list@mlist.mta.ca; Tue, 20 Sep 2011 08:02:12 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6907 Archived-At: Dear all, Given a 2-category C, there is a 2-category C' and a normal lax =20 functor from C to C' such that, for any normal lax functor from C to =20 a 2-category D, there is a unique strict 2-functor from C' to D which =20= makes the triangle commute. (To avoid any confusion: I take normal =20 lax functor to be what is defined in, say, p. 7 of the paper http://=20 arxiv.org/abs/0909.4229.) Gray, in "Formal Category Theory", I,4.23, Appendix A (p. 92), gives =20 an analogous universal construction with respect to general oplax =20 functors, and refers the reader to B=E9nabou's unpublished lectures as =20= a more general reference. I have seen a reference to Theorem 3.13 of =20 the Blackwell-Kelly-Power paper "Two-dimensional monad theory" (JPAA =20 59 (1989, 1-41), thanks to Matias del Hoyo for pointing that to me), =20 but I do not have it handy and I am unsure whether the general =20 theorem provides a much concrete description of the universal 2-=20 category in the particular case I am interested in (and I do not know =20= whether the normalized case falls into its range of application). Are there references dealing specifically with normalized (op)lax =20 functors? Is there an explicit description of this universal =20 construction I could refer to in the literature? Thanks in advance! Best wishes, Jonathan= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]