#
Fibrations of AU-contexts beget fibrations of toposes

##
Sina Hazratpour and Steven Vickers

Suppose an extension map U: T_1 -> T_0 in the 2-category
Con of contexts for arithmetic universes satisfies a Chevalley criterion for being an (op)fibration in Con.
If M is a model of T_0 in an elementary topos S with nno,
then the classifier p: S[T_1/M] -> S satisfies the representable definition of being an (op)fibration in the 2-category ETop
of elementary toposes (with nno) and geometric morphisms.

Keywords:
internal fibration, 2-fibration, context, bicategory, elementary topos, Grothendieck topos, arithmetic universe

2020 MSC: 18D30, 03G30, 18F10, 18C30, 18N10.

*Theory and Applications of Categories,*
Vol. 35, 2020,
No. 16, pp 562-593.

Published 2020-04-29.

http://www.tac.mta.ca/tac/volumes/35/16/35-16.pdf

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