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Categorification of Hopf algebras of rooted trees

By Joachim Kock

Centr. Eur. J. Math. 11 (2013), 401-422.
ArXiv:1109.5785.

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 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.

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Last updated: 2010-09-30 by Joachim Kock.