Geodesic
Fibrations of AU-contexts beget fibrations of toposes
Theory and applications of categories, Tome 35 (2020), pp. 562-593.

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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.
Publié le :
Classification : 18D30, 03G30, 18F10, 18C30, 18N10.
Keywords: internal fibration, 2-fibration, context, bicategory, elementary topos, Grothendieck topos, arithmetic universe 
@article{TAC_2020_35_a15,
     author = {Sina Hazratpour and Steven Vickers},
     title = {Fibrations of {AU-contexts} beget fibrations of toposes},
     journal = {Theory and applications of categories},
     pages = {562--593},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a15/}
}
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Sina Hazratpour; Steven Vickers. Fibrations of AU-contexts beget fibrations of toposes. Theory and applications of categories, Tome 35 (2020), pp. 562-593. http://geodesic.mathdoc.fr/item/TAC_2020_35_a15/