Categorification of Hopf algebras of rooted trees
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Categorification of Hopf algebras of rooted trees. / Kock, Joachim.
I: Central European Journal of Mathematics, Bind 11, Nr. 3, 03.2013, s. 401-422.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Categorification of Hopf algebras of rooted trees
AU - Kock, Joachim
PY - 2013/3
Y1 - 2013/3
N2 - 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.
AB - 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.
KW - Rooted trees
KW - Hopf algebras
KW - Categorification
KW - Monoidal categories
KW - Polynomial functors
KW - Finite sets
KW - QUANTUM-FIELD THEORY
KW - RENORMALIZATION
U2 - 10.2478/s11533-012-0152-1
DO - 10.2478/s11533-012-0152-1
M3 - Journal article
VL - 11
SP - 401
EP - 422
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
SN - 1895-1074
IS - 3
ER -
ID: 331501149