Iterated distributive laws

作者：Cheng Eugenia^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2011, 150: 459-487.

DOI：10.1017/S0305004110000599

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.