e/Distributive law between monads

Information
has gloss	eng: Suppose that (S,\mu^S,\eta^S) and (T,\mu^T,\eta^T) are two monads on a category C. In general, there is no natural monad structure on the composite functor ST. On the other hand, there is a natural monad structure on the functor ST if there is a distributive law of the monad S over the monad T.
lexicalization	eng: Distributive law between monads
instance of	e/Adjoint functors

Media
media:img	Distributive law monads mult1.png
media:img	Distributive law monads mult2.png
media:img	Distributive law monads unit1.png
media:img	Distributive law monads unit2.png