From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9031 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Grothendieck toposes Date: Wed, 9 Nov 2016 16:01:41 +0100 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1478961259 20221 195.159.176.226 (12 Nov 2016 14:34:19 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 12 Nov 2016 14:34:19 +0000 (UTC) Cc: wlawvere , categories@mta.ca To: Paul B Levy Original-X-From: majordomo@mlist.mta.ca Sat Nov 12 15:34:14 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 1c5ZNG-0000Iz-Ji for gsmc-categories@m.gmane.org; Sat, 12 Nov 2016 15:33:42 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:46648) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1c5ZMq-0008KL-62; Sat, 12 Nov 2016 10:33:16 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1c5ZMq-0004R8-PW for categories-list@mlist.mta.ca; Sat, 12 Nov 2016 10:33:16 -0400 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9031 Archived-At: On Wed, Nov 09, 2016 at 02:44:45PM +0000, Paul B Levy wrote: > > > On 09/11/16 10:48, Thomas Streicher wrote: >> What Eduardo means by "Giraud topos" is a category validating all >> conditions of the Giraud theorem with the exception of having a small >> generating family. These guys can be elementary toposes or not. >> There is Freyd's example where objects are set X with an ordinal >> indexed family of bijections from X to X > > So they don't form a class. > > Is there an example where the objects form a class? > > (I like categories to have this property!) That's not the problem. Objects do form a class! Eduardo rather thought that Freyd's example were not locally small. But it is! Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]