Monads and extended distributive laws

Ross Street – 23 February 2000

We begin by reviewing my talk The formal theory of monads revisited of 23 June 1999. For any bicategory K , we define a bicategory Mnde(K) with the same objects and morphisms as the bicategory Mnd(K) of my paper The formal theory of monads, but with more 2-cells. This turns out to make no difference to the formal theory of the construction of algebras as treated in my old paper. The point of this talk is to explain a more general concept of distributive law arising by looking at monads in Mnde(K). We give an example from the cohomology of groups to show that these extended distributive laws are genuinely more general.