A comparison of definitions of equivariant trees

Julia E. Bergner; Maxine E. Calle; David Chan; Angélica M. Osorno; Maru Sarazola

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arXiv · 2512.14956

A comparison of definitions of equivariant trees

Julia E. Bergner·Maxine E. Calle·David Chan·Angélica M. Osorno·Maru Sarazola

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Abstract

We show that various categories of trees can be modeled by Grothendieck constructions on categories of trees with a fixed set of leaves. We prove this result for the dendroidal category $\Omega$, the category $\Omega^G$ of trees with a $G$-action for a finite group $G$, and finally for the category of genuine equivariant trees $\Omega_G$ that has played an important role in recent work on genuine equivariant operads.

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Julia E. Bergner, Maxine E. Calle, David Chan, Angélica M. Osorno, Maru Sarazola. 2025-12-16. A comparison of definitions of equivariant trees. https://arxiv.org/abs/2512.14956

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