Berger-Joyal duality and traces I

2025/09/14 by Nicholas Cecil, Benjamin Cooper, Cecil, Nicholas +1
Physics and Astronomy · #Category Theory (math.CT) #Color Science and Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2509.11423

openalex publication_date 2025/09/14 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

We give a new proof that the opposite of Joyal's disk category D_n is Berger's wreath product category Θ_n = Δ\wr⋯\wrΔ. Our techniques continue to apply when the simplex category Δ is replaced by Connes' cyclic category Λ and some other crossed simplicial groups.

Citations

• On the duality between trees and disks
• (Infinity,2)-Categories and the Goodwillie Calculus I

Related

• Joyal's Suspension Functor on Θ and Kan's Combinatorial Spectra
• Generalised Joyal disks and Θ_d-colored (d+1)-operads
• Traces in symmetric monoidal categories
• Configurations spaces and Theta_n
• Comparing varieties generated by certain wreath products of groups