2-dimensional bifunctor theorems and distributive laws
Published 2020-10-15Version 1
In this paper we provide the conditions that need to be satisfied by two families of pseudofunctors with a common codomain for them to be collated into a bifunctor. We observe the similarities between these conditions and distributive laws of monads before providing a unified framework from which both of these results may be inferred. This we do by proving a version of the bifunctor theorem for lax functors. We show that these generalised distributive laws may be arranged into a 2-category Dist(B,C,D) and the collation of the distributive law into its associated bifunctor is given by a 2-functor into Lax(B x C, D). Furthermore, we show that the category Dist(B,C,D) is equivalent to Lax(B,Lax(C,D)) and that the collation 2-functor corresponds to uncurrying.