M Theory Lesson 113
One example of a distributive law is for the category of 2-globular sets, which are two dimensional globule diagrams of sources and targets $S_2 \Rightarrow S_1 \Rightarrow S_0$ in Set such that $ss = st$ and $ts = tt$. One monad is vertical composition, and the other is horizontal composition. The distributive law is just the interchange rule for bicategories. Iterating this idea, Cheng considers composition in n-categories using n-globular sets, a la Batanin.