Categorification of Hopf algebras of rooted trees

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)


We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring in the polynomial representation of the free monad on P. © 2013 Versita Warsaw and Springer-Verlag Wien.
Original languageEnglish
Pages (from-to)401-422
JournalCentral European Journal of Mathematics
Issue number3
Publication statusPublished - 1 Jan 2013


  • Categorification
  • Finite sets
  • Hopf algebras
  • Monoidal categories
  • Polynomial functors
  • Rooted trees

Fingerprint Dive into the research topics of 'Categorification of Hopf algebras of rooted trees'. Together they form a unique fingerprint.

  • Cite this

    Kock, J. (2013). Categorification of Hopf algebras of rooted trees. Central European Journal of Mathematics, 11(3), 401-422.