Geodesic
Diagonal Lemma for Presheaves on Elegant Reedy Categories
Theory and applications of categories, Tome 44 (2025), pp. 326-343

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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.
Publié le :
Classification : 18N40, 55U35 (primary), 18N45, 18N50 (secondary)
Keywords: diagonal lemma, Reedy category 
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     author = {Daniel Carranza and Krzysztof Kapulkin and Liang Ze Wong},
     title = {Diagonal {Lemma} for {Presheaves} on {Elegant} {Reedy} {Categories}},
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Daniel Carranza; Krzysztof Kapulkin; Liang Ze Wong. Diagonal Lemma for Presheaves on Elegant Reedy Categories. Theory and applications of categories, Tome 44 (2025), pp. 326-343. http://geodesic.mathdoc.fr/item/TAC_2025_44_a10/