From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9080 Path: news.gmane.org!.POSTED!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Fibred 2-category of Grothendieck toposes? Date: Tue, 17 Jan 2017 11:27:14 +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 1484663429 1505 195.159.176.226 (17 Jan 2017 14:30:29 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 17 Jan 2017 14:30:29 +0000 (UTC) Cc: Marta Bunge , Thomas Streicher To: Categories Original-X-From: majordomo@mlist.mta.ca Tue Jan 17 15:30:22 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1cTUm9-0007ue-De for gsmc-categories@m.gmane.org; Tue, 17 Jan 2017 15:30:17 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:40039) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cTUir-0006K5-FW; Tue, 17 Jan 2017 10:26:53 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cTUiS-0006yh-Rt for categories-list@mlist.mta.ca; Tue, 17 Jan 2017 10:26:28 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9080 Archived-At: This picks up a thread from a month ago, regarding an idea that Grothendieck toposes, interpreted generally as geometric morphisms bounded over the codomain base topos, might be treated in a 2- (or bi-)fibrational way over a variable base. I have now completed a paper "Arithmetic universes and classifying toposes" that does this. It is submitted to arXiv, and meanwhile available at http://www.cs.bham.ac.uk/~sjv/papersfull.php#AUClTop The arithmetic universes enter in via a logic interpretable in any elementary topos with nno. The "arithmetic" reasoning gives topos results that are base-independent and also "geometric", in the sense that when the base varies along a geometric morphism, the classifying topos transforms by pseudopullback. Steve. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]