Quillen model structures from models of HoTT
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A Quillen model category satisfying certain additional conditions can be shown to interpret homotopy type theory, as does for instance Voevodsky’s model in simplicial sets.
But the converse is also true: given a certain kind of abstract model of HoTT (as in the work of Orton & Pitts), one can endow the underlying category with a Quillen model structure, as was first shown by Sattler. A crucial role is played by the principle of univalence, which implies that the universe of fibrant objects is itself fibrant, by an argument due to Coquand.
This talk is part of the Category Theory Seminar series.
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