On the 2-categories of weak distributive laws

Gabriella Bohm, Stephen Lack, Ross Street

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    Abstract

    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 in. 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 k2×2.
    Original languageEnglish
    Pages (from-to)4567-4583
    Number of pages17
    JournalCommunications in Algebra
    Volume39
    Issue number12
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Eilenberg, Moore spectral sequences
    • arrow categories
    • monads
    • triples_theory of
    • weak distributive laws
    • weak lifting

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