Distributive laws between monads (triples) were defined by Jon Beck in the 1960s; see . They were generalized to monads in 2-categories and noticed to be monads in a 2-category of monads; see . Mixed distributive laws are comonads in the 2-category of monads ; if the comonad has a right adjoint monad, the mate of a mixed distributive law is an ordinary distributive law. Particular cases are the entwining operators between algebras and coalgebras; for example, see . Motivated by work on weak entwining operators (see  and ), we define and study a weak notion of distributive law for monads. In particular, each weak distributive law determines a wreath product monad (in the terminology of ); this gives an advantage over the mixed case.
|Number of pages||8|
|Journal||Theory and Applications of Categories|
|Publication status||Published - 28 Jan 2009|