From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6548 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Subobject Classifier Algorithm Date: Thu, 24 Feb 2011 17:14:44 -0500 Message-ID: Reply-To: "Fred E.J. Linton" 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 1298606797 17209 80.91.229.12 (25 Feb 2011 04:06:37 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 25 Feb 2011 04:06:37 +0000 (UTC) To: "Ellis D. Cooper" , Original-X-From: majordomo@mlist.mta.ca Fri Feb 25 05:06:32 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Psowp-0008K1-Qt for gsmc-categories@m.gmane.org; Fri, 25 Feb 2011 05:06:31 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42000) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Psowd-0001YT-HE; Fri, 25 Feb 2011 00:06:19 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PsowU-00036q-TT for categories-list@mlist.mta.ca; Fri, 25 Feb 2011 00:06:11 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6548 Archived-At: When "Ellis D. Cooper" asks, > What are the general rules for calculating the sub-object classifier > of a topos? Or, for what class of toposes is there an algorithm for > calculating the sub-object classifier of its members? I imagine the sort of response he hoped for is one like: In a presheaf topos, the suboject classifier Ω can be unraveled, from its universal property, by help of the Yoneda Lemma, as each of the = various values Ω(X) that Ω must take at an object X "is" the = set of natural transformations from hom(-, X) to Ω, which, in turn,= = "is" the set of subfunctors of the representable functor hom(-, X). I'll let others formulate similarly "algorhythmic" proposals for = other sorts of topoi (comonadic ones, sheaves, etc.). Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]