From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9028 Path: news.gmane.org!.POSTED!not-for-mail From: henry@phare.normalesup.org Newsgroups: gmane.science.mathematics.categories Subject: Re: Giraud_Elementary_? Date: Wed, 9 Nov 2016 10:13:24 +0100 Message-ID: References: Reply-To: henry@phare.normalesup.org NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Trace: blaine.gmane.org 1478702102 3303 195.159.176.226 (9 Nov 2016 14:35:02 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Wed, 9 Nov 2016 14:35:02 +0000 (UTC) Cc: "Categories list" To: "Eduardo Julio Dubuc" Original-X-From: majordomo@mlist.mta.ca Wed Nov 09 15:34:57 2016 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.28]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1c4TxV-0006Lt-W8 for gsmc-categories@m.gmane.org; Wed, 09 Nov 2016 15:34:38 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42716) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1c4Tx8-0000T9-GJ; Wed, 09 Nov 2016 10:34:14 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1c4Tx9-0008LB-0D for categories-list@mlist.mta.ca; Wed, 09 Nov 2016 10:34:15 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9028 Archived-At: Dear Eduardo Unless you are using a different statement of the Giraud's theorem than the one I have in mind, they are I think considerably more often called $\infty$-pretopos (like in the Elephant) or infinitary pretopos (like in the nLab) to avoid any confusion with an infinity categorical notion. I don't think I have ever encountered a different terminology (but I do like 'Giraud topos'). Regarding the example you are looking for, unless I'm missing something, the example 2.8 in SGA that you mentioned (the category sets endowed with smooth action of a large group) is also an elementary topos: sub-object classifier, exponential and power object are constructed exactly in the case of an ordinary group action topos and only involve a small quotient of the large group. So it answer you question. Bests, Simon > By Giraud topos I mean all the assumptions in Giraud's theorem, exept a > small set of generators. What Grothendieck call "faux topos". > > See SGA4 Exposse IV > Theoreme 1.2 (Giraud's theorem) and Example 2.8 (faux topos). > > best e.d. > > I guess I was wrong when I thought that "Giraud Topos" was established > terminology in the cat-list. > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]