A self-contained, brief and complete formulation of Voevodsky's Univalence Axiom

Abstract

In introductions to the subject for a general audience of mathematicians or logicians, the univalence axiom is typically explained by handwaving. This gives rise to several misconceptions, which cannot be properly addressed in the absence of a precise definition. In this short set of notes we give a complete formulation of the univalence axiom from scratch. The underlying idea of these notes is that they should be as concise as possible (and not more). They are not meant to be an Encyclopedia of Univalence.