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arXiv · 1607.06413

A cubical model of homotopy type theory

Steve Awodey
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Abstract

We construct an algebraic weak factorization system $(L, R)$ on the cartesian cubical sets, in which the canonical path object factorization $A \to A^I \to A\times A$ induced by the 1-cube $I$ is an $L$-$R$ factorization for any $R$-object $A$.

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Steve Awodey. 2016-07-21. A cubical model of homotopy type theory. https://arxiv.org/abs/1607.06413

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