Berger-Joyal duality and traces I
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909787159003136 |
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| author | Cecil, Nicholas Cooper, Benjamin |
| author_facet | Cecil, Nicholas Cooper, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Berger-Joyal duality and traces I Cecil, Nicholas Cooper, Benjamin Category Theory 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. |
| title | Berger-Joyal duality and traces I |
| topic | Category Theory |
| url | https://arxiv.org/abs/2509.11423 |