Homotopy type theory [Awodey and Warren, 2009; Voevodsky, 2011] is an extension of Martin-Löf’s intensional type theory [Martin-Löf, 1975; Nordström et al., 1990] with new principles such as Voevodsky’s univalence axiom and higher-dimensional inductive types [Lumsdaine and Shulman, 2013]. These extensions are interesting both from a computer science perspective, where they imbue the equality apparatus of type theory with new computational meaning, and from a mathematical perspective, where they allow higher-dimensional mathematics to be expressed cleanly and elegantly in type theory.