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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 22, 2012

Categorification of Hopf algebras of rooted trees

  • Joachim Kock EMAIL logo
From the journal Open Mathematics


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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Published Online: 2012-12-22
Published in Print: 2013-3-1

© 2013 Versita Warsaw

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