  A weak mixed distributive law (also called weak entwining structure) in a
2-category consists of a monad and a comonad, together with a 2-cell relating
them in a way which generalizes a mixed distributive law due to Beck. We show
that a weak mixed distributive law can be described as a compatible pair of a
monad and a comonad, in 2-categories extending, respectively, the 2-category of
comonads and the 2-category of monads. Based on this observation, we define a
2-category whose 0-cells are weak mixed distributive laws. In a 2-category K
which admits Eilenberg-Moore constructions both for monads and comonads, and in
which idempotent 2-cells split, we construct a fully faithful 2-functor from
this 2-category of weak mixed distributive laws to K^{2 x 2}.
