Profunctor Equipment in Haskell

Bartosz Milewski demonstrates a Haskell implementation of profunctor equipment from category theory, using standard library types like Functor and Profunctor to encode 2-cells and their compositions. The implementation allows compiler verification of categorical structures within a single category of Haskell types and functions, though a fully adequate version would require dependent types. The code includes definitions for horizontal and vertical composition of cells, unit laws, and companion and conjoint constructions.