English

Classification diagrams of simplicial categories

Algebraic Topology 2025-10-22 v2 Category Theory

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.

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

R2 v1 2026-06-28T14:31:28.623Z