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.
|Journal||Central European Journal of Mathematics|
|Publication status||Published - 1 Jan 2013|
- Finite sets
- Hopf algebras
- Monoidal categories
- Polynomial functors
- Rooted trees