A cubical model of homotopy type theory

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 $A$.

Lecture notes from a series of lectures for the Stockholm Logic group