From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6769 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: RE: stacks (was: size_question_encore) Date: Mon, 11 Jul 2011 18:20:42 -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 1310479288 11062 80.91.229.12 (12 Jul 2011 14:01:28 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 12 Jul 2011 14:01:28 +0000 (UTC) Cc: david.roberts@adelaide.edu.au, joyal.andre@uqam.ca, categories@mta.ca To: Marta Bunge Original-X-From: majordomo@mlist.mta.ca Tue Jul 12 16:01:19 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 1QgdWT-0002o4-Gi for gsmc-categories@m.gmane.org; Tue, 12 Jul 2011 16:01:13 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46969) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1QgdUN-0001q5-KS; Tue, 12 Jul 2011 10:59:03 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QgdUM-0006Gr-LW for categories-list@mlist.mta.ca; Tue, 12 Jul 2011 10:59:02 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6769 Archived-At: Is the "axiom of stack completions" related to the "axiom of small cardinality selection" used by Makkai to prove that the bicategory of anafunctors is cartesian closed? I think I recall a remark in Makkai's paper to the effect that the stack completion of a category C is at least morally the same as the category Ana(1,C) of "ana-objects" of C. Are there known examples of elementary toposes which violate the axiom of stack completions? On Mon, Jul 11, 2011 at 5:32 AM, Marta Bunge wrote= : > Concerning size matters, let me observe > that my construction of the stack completion (Bunge, Cahiers 1979) is > meaningful regardless of size questions, that is, for any base topos S. = =A0The > outcome, however, of applying it to an internal category need no longer = =A0be > internal. For this reason I introduce an "axiom of stack completions" > which guarantees that stack completions of internal categories be again > internal,and which is satisfied by any S a Grothehdieck topos. The questi= on of > stating such an axiom as an additional axiom to the ones for elementary t= oposes > was proposed as a problem by Lawvere in his Montreal lectures in 1974. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]