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Berger-Joyal duality and traces I (2509.11423v1)
Published 14 Sep 2025 in math.CT
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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