From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6783 Path: news.gmane.org!not-for-mail From: Marta Bunge Newsgroups: gmane.science.mathematics.categories Subject: RE: stacks (was: size_question_encore) Date: Wed, 13 Jul 2011 05:16:46 -0400 Message-ID: References: ,,,,<1210_1310496342_4E1C9656_1210_175_1_CAOvivQxdScpDev1nKES=2kfKTiQuerZStqTPmXtgs7EpSvVqjw@mail.gmail.com>,,<16988_1310523866_4E1D01DA_16988_150_1_CAOvivQw6wf9CV0bwd0SbOJ=_5umAcXhTGwVJbMp0tV3oHXk+SQ@mail.gmail.com> 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 1310580161 4221 80.91.229.12 (13 Jul 2011 18:02:41 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 13 Jul 2011 18:02:41 +0000 (UTC) To: Mike Shulman , Original-X-From: majordomo@mlist.mta.ca Wed Jul 13 20:02:37 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 1Qh3lc-0001Ag-Bp for gsmc-categories@m.gmane.org; Wed, 13 Jul 2011 20:02:36 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41801) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qh3jB-0003lN-L2; Wed, 13 Jul 2011 15:00:05 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qh3jA-0005zL-U9 for categories-list@mlist.mta.ca; Wed, 13 Jul 2011 15:00:04 -0300 In-Reply-To: <16988_1310523866_4E1D01DA_16988_150_1_CAOvivQw6wf9CV0bwd0SbOJ=_5umAcXhTGwVJbMp0tV3oHXk+SQ@mail.gmail.com> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6783 Archived-At: Dear Mike=2C Yes=2C AC is elementary.=A0Of course=2C so is ASC by the same token.=A0Quan= tifying over all epis is not a problem. Thanks for questioning me on that p= oint. I remembered incorrectly what the problem was. Bob Pare and I wanted = to posit something like the existence of a "representative (or universal) c= over" as an axiom (RC)=2C such that GT =3D> RC =3D> ASC=2C and also (ET + A= C) =3D> RC. We hoped to show that RC had good properties=2C and more import= antly=2C that Eff satisfied it but this did not work. What is still open is= whether Eff satisfies ASC.=A0 All the best=2C=A0 Marta=A0 =A0 > Date: Tue=2C 12 Jul 2011 19:24:25 -0700 > Subject: Re: categories: RE: stacks (was: size_question_encore) > From: mshulman@ucsd.edu > To: marta.bunge@mcgill.ca > CC: categories@mta.ca >=20 > I guess I misunderstood what you meant by "elementary". You wanted a > single statement that can be expressed in the internal logic of the > topos? Many other properties that people refer to as "elementary"=2C > such as the existence of finite limits or power objects=2C are defined > by quantifying over all objects and morphisms of the category in > question. Is AC "elementary"? >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]