Diagonal Lemma for Presheaves on Elegant Reedy Categories

Daniel Carranza, Krzysztof Kapulkin and Liang Ze Wong

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 paper, we observe that the standard proof of this fact works in greater generality, namely that of (elegant) Reedy categories.

Keywords: diagonal lemma, Reedy category

2020 MSC: 18N40, 55U35 (primary), 18N45, 18N50 (secondary)

Theory and Applications of Categories, Vol. 44, 2025, No. 11, pp 326-343.

Published 2025-04-30.

http://www.tac.mta.ca/tac/volumes/44/11/44-11.pdf

TAC Home