This coq library aims to formalize a substantial body of mathematics using the univalent point of view.

View the Project on GitHub UniMath/UniMath


This package is a repository for auxiliary material at a basic level, such as in the package “Foundations”, which doesn’t fit into one of the large categories represented by a later package. The material in this package is envisioned as being generally useful in any of the other later packages, so it comes second on the list of of packages in the Makefile.

Overview of contents


Some lemmas about quotient sets.


the proof that an equivalence, defined as a pair of maps with a pair of homotopies and an adjointness relation, is invertible.


A proof that squashing a two-element set yields an interval, together with the resulting proof of function extensionality for sections, using propositional truncation.