Abstract

Co-authors: Ulrik Buchholtz (TU Darmstadt), Jakob von Raumer (University of Nottingham) We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory, and contains many results in that area, among which are the computation of

, a formalization of Eilenberg-MacLane spaces and the adjunction of pointed maps and the smash product. We have a novel method of implementing higher inductive types (HITs), where we only take two HITs as primitives and add their computation rules to the kernel of Lean. We define all other HITs in terms of these two primitive ones. Other features include the use of cubical methods, a large algebraic hierarchy and category theory library. Related Linkshttps://github.com/leanprover/lean2/blob/master/hott/hott.md   The Lean HoTT libraryhttps://github.com/cmu-phil/Spectral   The Spectral Sequences project