From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9045 Path: news.gmane.org!.POSTED!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Fibred 2-category of Grothendieck toposes? Date: Fri, 02 Dec 2016 10:20:34 +0000 Message-ID: Reply-To: Steve Vickers NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1480682118 14421 195.159.176.226 (2 Dec 2016 12:35:18 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Fri, 2 Dec 2016 12:35:18 +0000 (UTC) User-Agent: Mozilla/5.0 (Windows; U; Windows NT 6.1; en-GB; rv:1.9.2.14) Gecko/20110221 Lightning/1.0b2 Thunderbird/3.1.8 To: Categories Original-X-From: majordomo@mlist.mta.ca Fri Dec 02 13:35:13 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 1cCn3Z-0002vL-A1 for gsmc-categories@m.gmane.org; Fri, 02 Dec 2016 13:35:13 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:51202) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cCn2x-00055r-QI; Fri, 02 Dec 2016 08:34:35 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cCn2y-0006W1-1X for categories-list@mlist.mta.ca; Fri, 02 Dec 2016 08:34:36 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9045 Archived-At: If "Grothendieck topos" means bounded geometric morphism into a given base S, then by allowing the base to vary we can get a 2-category GTop of Grothendieck toposes, fibred over some form of ETop (elementary toposes). This is because pseudopullbacks of bounded geometric morphisms along arbitrary geometric morphisms exist and are still bounded. (I say "some form of" ETop because it may be better to restrict the 2-cells downstairs to be isos, even though we certainly don't want to do the same upstairs. Also nnos are needed if classifying toposes are to exist.) Has anyone worked on that particular combination of bounded and unbounded? Steve Vickers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]