Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories
Algebraic Topology
2025-12-23 v2 Category Theory
Abstract
The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal simplicial sets. In this short note, we observe that the standard proof of this fact works for an arbitrary Eilenberg-Zilber category in place of the simplex category.
Keywords
Cite
@article{arxiv.2306.02217,
title = {Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories},
author = {Daniel Carranza and Chris Kapulkin and Liang Ze Wong},
journal= {arXiv preprint arXiv:2306.02217},
year = {2025}
}
Comments
version accepted for publication