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arXiv · 2509.11423

Berger-Joyal duality and traces I

Nicholas Cecil·Benjamin Cooper
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Abstract

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

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Nicholas Cecil, Benjamin Cooper. 2025-09-14. Berger-Joyal duality and traces I. https://arxiv.org/abs/2509.11423

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