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The diagonal lemma asserts that if a map of bisimplicial sets is a levelwiseweak equivalence in the Kan-Quillen model structure, then it induces a weakequivalence of the diagonal simplicial sets. In this short note, we observethat the standard proof of this fact works for an arbitrary Eilenberg-Zilbercategory in place of the simplex category.

Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories