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arXiv · 2610.38996

Graftings and cograftings for species

Pierre Clavier·Yannic Vargas
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Abstract

We introduce graftings and cograftings for vector species, modelled on the elementary operations of adjoining and deleting a root in a rooted forest. We relate these maps to operads, up and down operators, and obtain nontrivial balanced pairs, admitting pair of creation/annihilation operators with commuting relations. We establish universal properties for the species of rooted forests. Using Fock functors, we recover the classical Connes--Kreimer Hopf algebra, its noncommutative planar analogue, and Foissy's $q$-infinitesimal Hopf algebra.

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Pierre Clavier, Yannic Vargas. 2026-10-28. Graftings and cograftings for species. https://arxiv.org/abs/2610.38996

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