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Sheafifiable homotopy model categories

Tibor Beke
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Abstract

If a Quillen model category can be specified using a certain logical syntax (intuitively, ``is algebraic/combinatorial enough''), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site is a purely formal consequence of their being satisfied over the category of sets. Such data give rise to a functor from the category of topoi and geometric morphisms to Quillen model categories and Quillen adjunctions.

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Tibor Beke. 2001-02-11. Sheafifiable homotopy model categories. https://doi.org/10.1017/s0305004100004722

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