Categorification of Hopf algebras of rooted trees

Details Categorification of Hopf algebras of rooted trees Categorification of Hopf algebras of rooted trees

2011-09-27

arxiv.org/abs/1109.5785v1

Mathematics

Category Theory

28 pages. Does not compile with pdflatex due to dependency on the texdraw package

Scientific paper

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.

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