From: Steve Vickers <s.j.vickers@cs.bham.ac.uk>
To: Categories <categories@mta.ca>
Subject: Re: Composition of Fibrations and Quantification
Date: Sun, 8 Jun 2014 14:58:38 +0100 [thread overview]
Message-ID: <E1WuA6x-0004vo-DA@mlist.mta.ca> (raw)
In-Reply-To: <E1WtHHy-00055w-O5@mlist.mta.ca>
Some thoughts:
* The result about composition of fibrations holds in any 2-category with comma objects and 2-pullbacks, not just Cat. (Think of the Chevalley criterion for fibrations.)
* By duality on 2-cells it thus also applies to opfibrations, and hence to bifibrations.
* It is bifibration structure that gives you the left adjoints you ask for.
* For the right adjoints, look at the dual 2-category, where your fibrations become bifibrations.
Hence it seems to me that your conjectures are all true, and even generalize widely.
Steve.
> On 6 Jun 2014, at 10:47, Neil Ghani <neil.ghani@strath.ac.uk> wrote:
>
> Dear All
>
> We know that if p and q are fibrations, then their composition p.q is a fibration.
>
> But what about quantification … that is if reindexing along every morphism has a right/left adjoint in p and q, then does reindexing along every morphism in p.q have a right/left adjoint? Under some circumstances?
>
> Thanks for any thoughts
> Neil
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next prev parent reply other threads:[~2014-06-08 13:58 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2014-06-06 9:47 Neil Ghani
2014-06-08 13:58 ` Steve Vickers [this message]
2014-06-10 5:42 ` Richard Garner
2014-06-10 7:28 ` Thomas Streicher
2014-06-12 23:28 ` Claudio Hermida
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