From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7811 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: disjoint_coproducts_? Date: Thu, 25 Jul 2013 13:33:52 +0200 Message-ID: <20130725113352.GB10626@mathematik.tu-darmstadt.de> References: Reply-To: Thomas Streicher NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1374861883 4343 80.91.229.3 (26 Jul 2013 18:04:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 26 Jul 2013 18:04:43 +0000 (UTC) Cc: "'Eduardo J. Dubuc'" , "'Categories list'" To: Olivia Caramello Original-X-From: majordomo@mlist.mta.ca Fri Jul 26 20:04:44 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1V2mNf-0002vq-Gc for gsmc-categories@m.gmane.org; Fri, 26 Jul 2013 20:04:43 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:54298) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1V2mLr-0003Va-I9; Fri, 26 Jul 2013 15:02:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1V2mLr-0007gF-1P for categories-list@mlist.mta.ca; Fri, 26 Jul 2013 15:02:51 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7811 Archived-At: > Your statement is valid internally in SS, that is once formalized in the > internal language of the topos SS; this can be done in geometric logic, by > considering a (possibly infinitary) disjunction over all the arrows f: C > ---> X for C in CC (interpreted by the arrows Ff in SS) and existential > quantifications. If you want a statement valid 'externally', you should > instead use generalized elements in SS and epimorphic families involving > their domains. Since CC is internal to SS which is assumed as different from Set it doesn't make sense to consider an infinite disjunction over all arrows f: C --> X for C in CC. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]