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# Univalence for inverse diagrams and homotopy canonicity

@article{Shulman2015UnivalenceFI, title={Univalence for inverse diagrams and homotopy canonicity}, author={Michael Shulman}, journal={Mathematical Structures in Computer Science}, year={2015}, volume={25}, pages={1203-1277} }

- Published 2015 in Mathematical Structures in Computer Science
DOI:10.1017/S0960129514000565

We describe a homotopical version of the relational and gluing models of type theory, and generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy theory on inverse diagrams, and relies on the fact that Reedy fibrant diagrams correspond to contexts of a certain shape in type theory. This has two main applications. First, by considering inverse diagrams in Voevodsky’s univalent model in simplicial sets, we obtain new models of univalence in a number of (∞, 1… CONTINUE READING

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