Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories
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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