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From: "Prof. Peter Johnstone"
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Subject: Re: Equality and fibration
Date: Wed, 2 Jun 2010 10:34:42 +0100 (BST)
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On Mon, 31 May 2010, Joyal, Andr=E9 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 categ=
ory.
> Can you?
>
> Andr=E9
>
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
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