The formal theory of monads II

Stephen Lack*, Ross Street

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    84 Citations (Scopus)


    We give an explicit description of the free completion EM(K) of a 2-category K under the Eilenberg-Moore construction, and show that this has the same underlying category as the 2-category Mnd(K) of monads in K. We then demonstrate that much of the formal theory of monads can be deduced using only the universal property of this completion, provided that one is willing to work with EM(K) as the 2-category of monads rather than Mnd(K). We also introduce the wreaths in K; these are the objects of EM(EM(K)), and are to be thought of as generalized distributive laws. We study these wreaths, and give examples to show how they arise in a variety of contexts.

    Original languageEnglish
    Pages (from-to)243-265
    Number of pages23
    JournalJournal of Pure and Applied Algebra
    Issue number1-3
    Publication statusPublished - 8 Nov 2002


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