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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0152-1,
author = {Joachim Kock},
title = {Categorification of Hopf algebras of rooted trees},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {401-422},
zbl = {1270.16030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0152-1}
}
Joachim Kock. Categorification of Hopf algebras of rooted trees. Open Mathematics, Tome 11 (2013) pp. 401-422. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0152-1/
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