Weak distributive laws

Ross Street*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    19 Citations (Scopus)
    30 Downloads (Pure)


    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 languageEnglish
    Pages (from-to)313-320
    Number of pages8
    JournalTheory and Applications of Categories
    Publication statusPublished - 28 Jan 2009

    Bibliographical note

    Copyright the Author(s) [2009]. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


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