2 Jun
2010
2 Jun
'10
9:34 a.m.
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/ ]