From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8580 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor product of left exact morphisms Date: Fri, 27 Mar 2015 10:08:47 +1100 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1427460197 10611 80.91.229.3 (27 Mar 2015 12:43:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 27 Mar 2015 12:43:17 +0000 (UTC) To: =?ISO-8859-1?Q?Joyal=2C=20Andr=E9?= , Categories list Original-X-From: majordomo@mlist.mta.ca Fri Mar 27 13:43:10 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YbTbE-0004sQ-TG for gsmc-categories@m.gmane.org; Fri, 27 Mar 2015 13:42:57 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:57475) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YbTak-0005Sc-AU; Fri, 27 Mar 2015 09:42:26 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YbTai-0002cg-87 for categories-list@mlist.mta.ca; Fri, 27 Mar 2015 09:42:24 -0300 In-Reply-To: <8C57894C7413F04A98DDF5629FEC90B1137B097E@Pli.gst.uqam.ca> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8580 Archived-At: Thanks, Andr=E9, that's helpful. This: > In general, if a topos $mathcal{E}$ > classifies the models of a geometric theory T, there is > another topos $mathcal{E}$ which classifies variable families > of models of T: it is the *bagdomain* of $mathcal{E}$ > introduced by Johnstone. See the Elephant vol. I Proposition 4.4.16. is particularly good. I knew about the bagdomain, but didn't connect it to my question. However, I think I want a non-transitive torsor to be a right G-set with a free action, but which is also inhabited. This means passing to a subtopos of [X, Set], where X is as before the category of finitely generated free G^op sets. Looking at the calculation I made before, I think I got it wrong. I must pass to the topology generated by making 0 ----> G into a cocover in X. But then I must also make every pushout of this into a cocover, and every composite of such pushouts into a cocover. So, in the end, I think the classifying topos should be Sh(X^op) for the topology whose cocovers are the coproduct injections in X. In other words, I take the Lawvere theory of G^op-sets, and take sheaves on it for the topology given by the project projections. Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]