From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7542 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Fibred toposes Date: Wed, 19 Dec 2012 12:38:48 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1355942258 16450 80.91.229.3 (19 Dec 2012 18:37:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 19 Dec 2012 18:37:38 +0000 (UTC) Cc: "categories@mta.ca list" To: David Roberts Original-X-From: majordomo@mlist.mta.ca Wed Dec 19 19:37:53 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.32]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1TlOWc-0005vO-Ts for gsmc-categories@m.gmane.org; Wed, 19 Dec 2012 19:37:51 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:39066) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1TlORC-0005fP-I6; Wed, 19 Dec 2012 14:32:14 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1TlOWK-00062x-Kz for categories-list@mlist.mta.ca; Wed, 19 Dec 2012 14:37:32 -0400 User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.7; rv:12.0) Gecko/20120428 Thunderbird/12.0.1 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7542 Archived-At: Already in 1962-63 in SGA4 was considered and developed the concept of Fibred Topos (SLN 270 VI 7. p 273). Recall that in SGA4, Topos (or U-topos) = your Bounded Topos. If you want to consider a different concept of fibred topos, it is not correct to use the same name. best eduardo On 18/12/12 03:28, David Roberts wrote: > Dear all, > > I'm thinking about fibred toposes, and I was wondering if there any > references people can suggest? The following are some pitifully vague > thoughts. > > One particular problem I'm thinking about is whether there is a > generic fibred topos, which is the analogue of the generic discrete > fibration Set_* --> Set or the generic fibration 1 / Cat --> Cat. > > Something like the 2-category Topos of bounded toposes and geometric > morphisms (and whatever 2-arrows are appropriate). The objects of this > are bounded geometric morphisms, arrows are 2-commutative squares. > Then take the 2-category over this where the objects are bounded > toposes E --> S with a point Set --> E, or possibly an S-point S --> > E, and arrows those geometric morphisms which preserve the point up to > natural transformation. > > Ideally I'd then like to consider 2-functors T^op -->Topos to be > equivalent to (bounded) fibred toposes over T. > > Best, > > David Roberts > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]