%0 Journal Article
%T Categorification of Hopf algebras of rooted trees
%A Joachim Kock
%J Mathematics
%D 2011
%I arXiv
%X 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 H_0). 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.
%U http://arxiv.org/abs/1109.5785v2