From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6772 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: RE: stacks (was: size_question_encore) Date: Tue, 12 Jul 2011 07:33:46 -0700 Message-ID: References: Reply-To: Michael Shulman 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 1310495705 21420 80.91.229.12 (12 Jul 2011 18:35:05 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 12 Jul 2011 18:35:05 +0000 (UTC) Cc: David Roberts , joyal.andre@uqam.ca, categories@mta.ca To: Marta Bunge Original-X-From: majordomo@mlist.mta.ca Tue Jul 12 20:35:00 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 1QghnP-0005CM-Mm for gsmc-categories@m.gmane.org; Tue, 12 Jul 2011 20:34:59 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45021) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qghkr-0006An-9a; Tue, 12 Jul 2011 15:32:21 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qghkq-0001VL-Hq for categories-list@mlist.mta.ca; Tue, 12 Jul 2011 15:32:20 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6772 Archived-At: On Tue, Jul 12, 2011 at 5:30 AM, Marta Bunge wrote= : > I am glad that Makkai is now aware of this fact, which gives a universal = flavor to his subject, whatever "morally" means. The paper I was referring to is the one that first introduced anafunctors, so I think he's been aware of it since the beginning (I suspect it was a primary motivation, even). The word "morally" was my own weasel word, to cover the fact that I didn't have time to look up the paper and remind myself what precisely he actually wrote. (-: > As for there being an example of an elementary topos which does not satis= fy =A0the "axiom of stack completions", Joyal gave one long ago and Lawvere= mentioned it in his 1974 Montreal lectures. Take a group G with a proper c= lass of subgroups having a small index in G. The topos [G, Sets] is an exam= ple. Ah, thanks. That makes sense. The question about the effective topos is also intriguing! Are there any interesting non-Grothendieck elementary toposes which are known to satisfy the axiom of stack completions? (By "interesting" I mean to exclude toposes such as the category of sets smaller than some strong limit cardinal -- not to say that such toposes are not interesting for other purposes.) Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]