Decomposing the Univalence Axiom
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This paper investigates the univalence axiom in intensional Martin-Löf type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then we present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms are easier to verify in potential models of univalent type theory and show this is the case for cubical sets. Finally we show how this decomposition is relevant to an open problem in type theory.
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