Iterated distributive laws

Abstract

Abstract We give a framework for combining n monads on the same category via distributive laws satisfying Yang–Baxter equations, extending the classical result of Beck which combines two monads via one distributive law. We show that this corresponds to iterating n -times the process of taking the 2-category of monads in a 2-category, extending the result of Street characterising distributive laws. We show that this framework can be used to construct the free strict n -category monad on n -dimensional globular sets; we first construct for each i a monad for composition along bounding i -cells, and then we show that the interchange laws define distributive laws between these monads, satisfying the necessary Yang–Baxter equations.