From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9050 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Fibred 2-category of Grothendieck toposes? Date: Sun, 4 Dec 2016 13:00:48 +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 1480984887 16826 195.159.176.226 (6 Dec 2016 00:41:27 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 6 Dec 2016 00:41:27 +0000 (UTC) Cc: categories@mta.ca To: Steve Vickers Original-X-From: majordomo@mlist.mta.ca Tue Dec 06 01:41:23 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 1cE3ow-0003i6-Bq for gsmc-categories@m.gmane.org; Tue, 06 Dec 2016 01:41:22 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:57605) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cE3oX-0006kB-Vt; Mon, 05 Dec 2016 20:40:57 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cE3oa-0004Pl-1Q for categories-list@mlist.mta.ca; Mon, 05 Dec 2016 20:41:00 -0400 Content-Disposition: inline In-Reply-To: <2C7348C8-AAE0-4F33-A2B2-A4E112740F25@cs.bham.ac.uk> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9050 Archived-At: Steve, we are speaking about different things. Pullbacks of bgm's along arbitrary gm's are described sufficiently well [Joh77] and in the Elephant. But what I have commented on was how to appropriately captured change of base when studying topose sover a base topos. I am working on the "algebraic" side whereas you think on the "geometric" side. Reindexing in terms of the algebraic view is given by precomposition but reindexing in terms of the geometric view is postcomposition. What I want to say is that pullbacks in Top are very different from the change of base for relative topos theory. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]