Polynomial monads and delooping of mapping spaces

Michael A. Batanin, Florian De Leger

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    We extend some classical results - such as Quillen's Theorem A, the Grothendieck construction, Thomason's theorem and the characterisation of homotopically cofinal functors – from the homotopy theory of small categories to polynomial monads and their algebras.

    As an application we give a categorical proof of the Dwyer–Hess and Turchin results concerning the explicit double delooping of spaces of long knots.

    Original languageEnglish
    Pages (from-to)1521-1576
    Number of pages56
    JournalJournal of Noncommutative Geometry
    Issue number4
    Early online date20 Jan 2019
    Publication statusPublished - 2019


    • Operad
    • polynomial monad
    • internal algebra
    • delooping
    • space of knots


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