From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: "Joyal, André" <joyal.andre@uqam.ca>
Cc: Categories list <categories@mta.ca>
Subject: Re: Equality and fibration
Date: Wed, 2 Jun 2010 10:34:42 +0100 (BST) [thread overview]
Message-ID: <E1OJnbe-0006BC-Qm@mailserv.mta.ca> (raw)
In-Reply-To: <E1OJQEc-0002Bi-A2@mailserv.mta.ca>
On Mon, 31 May 2010, Joyal, André wrote:
> Dear category theorists,
>
> I have not been able to define the notion of Grothendieck fibration
> without using the equality relation between the objects of the base category.
> Can you?
>
> André
>
No, because an equivalence of categories is not a Grothendieck fibration
in general. However, there is a weaker version of the notion where one
replaces equality by the existence of a (specified) isomorphism; there
are some comments about this in my paper "Fibrations and partial
products in a 2-category" in Applied Categorical Structures 1 (1993),
141--179.
Peter Johnstone
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-06-02 9:34 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-05-29 21:18 isomorphisms Eduardo J. Dubuc
2010-05-30 15:11 ` isomorphisms Colin McLarty
2010-05-31 2:51 ` isomorphisms Michael Shulman
2010-06-01 3:26 ` Equality and fibration Joyal, André
2010-06-02 9:34 ` Prof. Peter Johnstone [this message]
2010-06-01 12:57 ` Peter LeFanu Lumsdaine
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