Univalent foundations is a modern approach to the foundations of mathematics that reconstructs mathematical objects using types rather than traditional sets, significantly influenced by homotopy theory and higher category theory. It was developed by Vladimir Voevodsky with a principal aim of facilitating computer verification of mathematical proofs, reducing the risk of errors and making formalized mathematics more invariant under equivalence rather than mere isomorphism or equality.
Sources
https://en.wikipedia.org/wiki/Univalent_foundations https://arxiv.org/pdf/1711.01477