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arXiv · 1109.5785

Categorification of Hopf algebras of rooted trees

Joachim Kock
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Abstract

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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Joachim Kock. 2012-04-28. Categorification of Hopf algebras of rooted trees. https://arxiv.org/abs/1109.5785

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