A comparison of definitions of equivariant trees

2025/12/16 by Bergner, Julia E., Calle, Maxine E., Chan, David +2
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · doi:10.48550/arxiv.2512.14956

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 Ω, the category Ω^G of trees with a G-action for a finite group G, and finally for the category of genuine equivariant trees Ω_G that has played an important role in recent work on genuine equivariant operads.

Citations

• Partition complexes and trees
• 2-Dimensional Categories
• Operadic multiplications in equivariant spectra, norms, and transfers
• On the equivalence between Lurie's model and the dendroidal model for\n infinity-operads

Related

• Equivariant Trees and Partition Complexes
• Equivalence of models for equivariant (∞, 1)-categories
• On equivariant derived categories
• Elmendorf constructions for G-categories and G-posets
• Equivariant A-theory