University of Chicago
Department of Mathematics

We address the question of how elegantly to combine a number of different structures on a category, such as finite product structure, monoidal structure, and colimiting structure. Extending work of Marmolejo and Lack, we develop the definition of a pseudo-distributive law between pseudo-monads, and we show how the definition and the main theorems about it may be used to model several such structures simultaneously. Specifically, we address the relationship between pseudo-distributive laws and the lifting of one pseudo-monad to the 2-category of algebras and to the Kleisli bicategory of another. This generalises the main result of the theory of ordinary distributive laws between monads; I will begin the talk with an overview of this theory before presenting its generalisation.