From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6779 Path: news.gmane.org!not-for-mail From: Marta Bunge Newsgroups: gmane.science.mathematics.categories Subject: RE: stacks (was: size_question_encore) Date: Tue, 12 Jul 2011 15:56:44 -0400 Message-ID: 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 1310579847 2213 80.91.229.12 (13 Jul 2011 17:57:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 13 Jul 2011 17:57:27 +0000 (UTC) To: Mike Shulman , Original-X-From: majordomo@mlist.mta.ca Wed Jul 13 19:57:23 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qh3gX-0006Mj-Rl for gsmc-categories@m.gmane.org; Wed, 13 Jul 2011 19:57:22 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49451) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qh3e8-0002uM-Sa; Wed, 13 Jul 2011 14:54:52 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qh3e8-0005o3-7b for categories-list@mlist.mta.ca; Wed, 13 Jul 2011 14:54:52 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6779 Archived-At: Dear Mike=2C=A0 > > Does it not work to say that every internal category admits a weak > equivalence functor to an internal category which is a stack? Sure. This is so by Corollary 2.11 in Bunge-Pare. No problem with internal = categories or internal weak equivalence functors of course. But how does on= e internalize the notion of a stack? It comes down to parametrizing all epi= morphisms in the topos itself.=A0 All the best=2CMarta ---------------------------------------- > Date: Tue=2C 12 Jul 2011 11:45:41 -0700 > Subject: Re: categories: RE: stacks (was: size_question_encore) > From: mshulman@ucsd.edu > To: marta.bunge@mcgill.ca > CC: david.roberts@adelaide.edu.au=3B joyal.andre@uqam.ca=3B categories@mt= a.ca > > On Tue=2C Jul 12=2C 2011 at 7:56 AM=2C Marta Bunge wrote: >> As for stacks being the primary motivation Makkai had for anafunctors= =2C that is not the impression I got from people attending his course=2C > > Okay=2C thanks for the correction. > >> I forgot to mention that an elementary formulation of ASC ("axiom of st= ack completions") is till missing. > > Does it not work to say that every internal category admits a weak > equivalence functor to an internal category which is a stack? > > Mike = [For admin and other information see: http://www.mta.ca/~cat-dist/ ]