In category theory, an abstract branch of mathematics, distributive laws between monads are a way to express abstractly that two algebraic structures distribute one over the other one. Suppose that and are two monads on a category C. In general, there is no natural monad structure on the composite functor ST. However, there is a natural monad structure on the functor ST if there is a distributive law of the monad S over the monad T. Formally, a distributive law of the monad S over the monad T is a natural transformation such that the diagrams commute. This law induces a composite monad ST with
