From: Steve Vickers <s.j.vickers@cs.bham.ac.uk>
To: Categories <categories@mta.ca>
Subject: Fibred 2-category of Grothendieck toposes?
Date: Fri, 02 Dec 2016 10:20:34 +0000 [thread overview]
Message-ID: <E1cCn2y-0006W1-1X@mlist.mta.ca> (raw)
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/ ]
next reply other threads:[~2016-12-02 10:20 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-12-02 10:20 Steve Vickers [this message]
[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
[not found] <8135_1480682187_58416ACB_8135_508_1_E1cCn2y-0006W1-1X@mlist.mta.ca>
2016-12-02 13:30 ` Marta Bunge
2017-01-17 11:27 Steve Vickers
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