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arXiv · 1710.10941

The univalence axiom in cubical sets

Marc Bezem·Thierry Coquand·Simon Huber
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Abstract

In this note we show that Voevodsky's univalence axiom holds in the model of type theory based on symmetric cubical sets. We will also discuss Swan's construction of the identity type in this variation of cubical sets. This proves that we have a model of type theory supporting dependent products, dependent sums, univalent universes, and identity types with the usual judgmental equality, and this model is formulated in a constructive metatheory.

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Marc Bezem, Thierry Coquand, Simon Huber. 2017-10-30. The univalence axiom in cubical sets. https://arxiv.org/abs/1710.10941

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