Homotopy Type Theory

This brand is dedicated to the investigation of Homotopy Type Theory, a new field of study that combines Martin-Löf's system of intensional, constructive type theory with abstract homotopy theory. The aim of this brand is to collect and disseminate research, resources, and tools related to Homotopy Type Theory, providing a valuable resource for those involved in its study. Propositional equality is interpreted as homotopy, and type isomorphism is interpreted as homotopy equivalence within this theory.

By applying logical constructions in type theory to spaces, this brand enables the exploration of homotopy-invariant constructions. Additionally, the brand is closely tied to the Univalent Foundations program, which aims to establish a comprehensive, computational foundation for mathematics based on the homotopical interpretation of type theory. With the help of the automated proof assistant Coq, the Univalent Foundations program is currently being implemented by researchers in parallel with their pursuit of Homotopy Type Theory