From: Steve Vickers <s.j.vickers@cs.bham.ac.uk>
To: Categories <categories@mta.ca>
Cc: Marta Bunge <martabunge@hotmail.com>,
Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
Subject: Fibred 2-category of Grothendieck toposes?
Date: Tue, 17 Jan 2017 11:27:14 +0000 [thread overview]
Message-ID: <E1cTUiS-0006yh-Rt@mlist.mta.ca> (raw)
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/ ]
next reply other threads:[~2017-01-17 11:27 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-01-17 11:27 Steve Vickers [this message]
[not found] <8135_1480682187_58416ACB_8135_508_1_E1cCn2y-0006W1-1X@mlist.mta.ca>
2016-12-02 13:30 ` Marta Bunge
-- strict thread matches above, loose matches on Subject: below --
2016-12-02 10:20 Steve Vickers
[not found] ` <2C7348C8-AAE0-4F33-A2B2-A4E112740F25@cs.bham.ac.uk>
2016-12-04 12:00 ` Thomas Streicher
[not found] ` <98602071-6A60-42DF-BFC7-2C4E2745F980@cs.bham.ac.uk>
2016-12-05 10:26 ` Thomas Streicher
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