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arXiv · 2306.02217

Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories

Daniel Carranza·Chris Kapulkin·Liang Ze Wong
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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.

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Daniel Carranza, Chris Kapulkin, Liang Ze Wong. 2023-06-04. Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories. https://arxiv.org/abs/2306.02217

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