Homotopy theory for algebras over polynomial monads

M. A. Batanin, C. Berger

    Research output: Contribution to journalArticle

    12 Citations (Scopus)


    We study the existence and left properness of transferred model structures for “monoid-like” objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular, higher operads, properads and PROP’s. All these structures can be realised as algebras over polynomial monads. We give a general condition for a polynomial monad which ensures the existence and (relative) left properness of a transferred model structure for its algebras. This condition is of a combinatorial nature and singles out a special class of polynomial monads which we call tame polynomial. Many important monads are shown to be tame polynomial.

    Original languageEnglish
    Pages (from-to)148-253
    Number of pages106
    JournalTheory and Applications of Categories
    Issue number6
    Publication statusPublished - 6 Feb 2017


    • quillen model category
    • polynomial monad
    • coloured operad
    • graph

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