Categorification of Hopf algebras of rooted trees
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Central European Journal of Mathematics |
Volume | 11 |
Issue number | 3 |
Pages (from-to) | 401-422 |
Number of pages | 22 |
ISSN | 1895-1074 |
DOIs | |
Publication status | Published - Mar 2013 |
Externally published | Yes |
- Rooted trees, Hopf algebras, Categorification, Monoidal categories, Polynomial functors, Finite sets, QUANTUM-FIELD THEORY, RENORMALIZATION
Research areas
ID: 331501149