From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6500 Path: news.gmane.org!not-for-mail From: Marta Bunge Newsgroups: gmane.science.mathematics.categories Subject: Re: Fibrations in a 2-Category Date: Sat, 29 Jan 2011 14:20:36 -0500 Message-ID: References: <20110129190220.DC8A8ADFB@mailscan3.ncs.mcgill.ca> Reply-To: Marta Bunge 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 1296427859 10872 80.91.229.12 (30 Jan 2011 22:50:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 30 Jan 2011 22:50:59 +0000 (UTC) To: Original-X-From: majordomo@mlist.mta.ca Sun Jan 30 23:50:54 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Pjg6f-0005Il-9R for gsmc-categories@m.gmane.org; Sun, 30 Jan 2011 23:50:53 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:44080) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Pjg6W-0004xZ-2e; Sun, 30 Jan 2011 18:50:44 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Pjg6S-0000bJ-5W for categories-list@mlist.mta.ca; Sun, 30 Jan 2011 18:50:40 -0400 In-Reply-To: <20110129190220.DC8A8ADFB@mailscan3.ncs.mcgill.ca> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6500 Archived-At: Dear Mike=2C I have no objection to anything you actually say. Yes=2C of course any func= tor is an anafunctor and=2C under AC=2C every anafunctor is isomorphic to a= functor. But that is what I meant.=A0It was just that=2C emphasizing the f= act that anafunctors generalize functors (without AC)=2C I wanted to note t= hat distributors (not necesarily representable) also do=2C even with AC=2C = and that in this alone lies their importance=2C plus the fact that they can= be composed etc. I do not intend to modify your excellent exposition of an= afunctors=2C a subject that I "learnt" just by reading it. I did not mean i= t as a criticism. Many thanks=2C Marta > Date: Sat=2C 29 Jan 2011 11:02:19 -0800 > Subject: Re: categories: Re: Fibrations in a 2-Category > From: mshulman@ucsd.edu > To: marta.bunge@mcgill.ca > CC: categories@mta.ca >=20 > Dear Marta=2C >=20 > The discussion of the equivalence in the nLab article you mention was > added 5 days ago by me=2C by extracting and condensing a bit from > Jean's=2C my=2C and David's emails a week ago. I thought this discussion > interesting enough that it ought to be preserved. >=20 > On Sat=2C Jan 29=2C 2011 at 9:45 AM=2C Marta Bunge wrote: >> In that article=2C it is furthermore pointed out that each version has i= ts advantages over the other=2C and that therefore both are of interest for= category theory in a topos S without AC=2C where they generalize ordinary = functors.=A0But=2C even in the presence of AC=2C distributors (profunctors)= generalize ordinary functors=2C a fact that I have known for 45 years=2C w= hereas anafunctors do not. >=20 > This confused me for a minute until I realized you probably meant > "generalize" to mean "strictly generalize." (It is of course still > true under AC that every functor is an anafunctor=3B the difference > being rather that under AC every anafunctor is isomorphic to a > functor.) >=20 > As David pointed out=2C since the nLab is a wiki=2C anyone who feels the > discussion currently existing there has defects should feel free to > take it upon themselves to remedy those defects. >=20 > Best=2C > Mike = [For admin and other information see: http://www.mta.ca/~cat-dist/ ]