DISTRIBUTIVE LAW, COMMUTATOR THEORY AND YANG-BAXTER EQUATION
A monad on the category being given, it is well known that a distributive law is the same thing as an extension of the monad R up to a monad on the category of R-algebras. We show here that the distributive law d satisfies the Yang-Baxter equation if and only if it can be extended up to a distributive law This gives rise, for all to a monad on The categories of algebras are characterized and shown to determine a tower of monadic functors:
Examples dealing with Commutator theory are produced.
distributive laws, algebras of monads, Yang-Baxter equations, descent theory.