Classification diagrams of simplicial categories
Algebraic Topology
2025-10-22 v2 Category Theory
Abstract
We show that the classification diagram of a relative -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.
Keywords
Cite
@article{arxiv.2401.16855,
title = {Classification diagrams of simplicial categories},
author = {Kensuke Arakawa},
journal= {arXiv preprint arXiv:2401.16855},
year = {2025}
}
Comments
identical to the published version except for formatting differences