Berger-Joyal duality and traces I

Nicholas Cecil; Benjamin Cooper

doi:10.48550/arxiv.2509.11423

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Berger-Joyal duality and traces I

Nicholas Cecil and Benjamin Cooper

ArXiv.org

Cornell University

09/14/2025

DOI: 10.48550/arxiv.2509.11423

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https://doi.org/10.48550/arXiv.2509.11423View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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

Mathematics - Category Theory

Details

Title: Subtitle: Berger-Joyal duality and traces I
Creators: Nicholas Cecil - University of Iowa
Benjamin Cooper - University of Iowa
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2509.11423
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 09/14/2025
Academic Unit: Mathematics
Record Identifier: 9984963627102771

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