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On the Inadequacy of the Projective Structure with Respect to the Univalence Axiom (1712.02652v3)
Published 6 Dec 2017 in math.CT, math.AT, and math.LO
Abstract: In this article the author endows the functor category [B(C2),Gpd] with the structure of a type-theoretic fibration category with a universe using the projective fibrations. It offers a new model of Martin-L\"of type theory with dependent sums, dependent products, identity types and a universe. It turns out that this universe, the natural candidate that lifts the univalent universe of small discrete groupoids in the groupoid model of Hofmann and Streicher, is not univalent.
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