Monads with arities and their associated theories

Clemens Berger, Paul-André Melliès, Mark Weber

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    41 Citations (Scopus)


    After a review of the concept of "monad with arities" we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere's algebraic theories to a general correspondence between monads and theories for a given category with arities. As an application we determine arities for the free groupoid monad on involutive graphs and recover the symmetric simplicial nerve characterisation of groupoids.
    Original languageEnglish
    Pages (from-to)2029-2048
    Number of pages20
    JournalJournal of Pure and Applied Algebra
    Issue number8-9
    Publication statusPublished - 2012


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