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Parametricity, Automorphisms of the Universe, and Excluded Middle

, USA 2 Auke B. Booij School of Computer Science, University of Birmingham , Birmingham , UK 3 Peter LeFanu Lumsdaine Mathematics Department, Stockholm University , Stockholm , Sweden 4 Marti?n H. Escardo

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- 1039 , 2015 . arXiv:1303 .0584, doi:10.1017/S0960129514000486. Benedikt Ahrens , Peter LeFanu Lumsdaine , and Vladimir Voevodsky . Categorical structures for type theory in univalent foundations , 2017

Categorical Structures for Type Theory in Univalent Foundations

In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in the setting of univalent foundations, where the relationships between them can be stated more transparently. Specifically, we construct maps...