## Abstract

Distributive laws between monads (triples) were defined by Jon Beck in the 1960s; see [1]. They were generalized to monads in 2-categories and noticed to be monads in a 2-category of monads; see [2]. Mixed distributive laws are comonads in the 2-category of monads [3]; 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 [4]. Motivated by work on weak entwining operators (see [5] and [6]), 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 [7]); this gives an advantage over the mixed case.

Original language | English |
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Pages (from-to) | 313-320 |

Number of pages | 8 |

Journal | Theory and Applications of Categories |

Volume | 22 |

Publication status | Published - 28 Jan 2009 |