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arXiv · 2401.16855

Classification diagrams of simplicial categories

Kensuke Arakawa
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Abstract

We show that the classification diagram of a relative $\infty$-category arising from a relative simplicial category is equivalent to the levelwise nerve. Applications include the comparison of the diagonal of the levelwise nerve and the homotopy coherent nerve, and a result on the levelwise localizations of simplicial categories.

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Kensuke Arakawa. 2024-01-30. Classification diagrams of simplicial categories. https://arxiv.org/abs/2401.16855

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