Categorification of Hopf algebras of rooted trees

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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


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