HOMOLOGY OF CATEGORIES VIA POLYGRAPHIC RESOLUTIONS

Léonard Guetta (1)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

In this paper, we extend a result of Lafont and Métayer and prove that the polygraphic homology of a small category, defined in terms of polygraphic resolutions in the category ωCat of strict ω-categories, is naturally isomorphic to the homology of its nerve. Along the way, we prove some results on homotopy colimits with respect to the Folk model structure and deduce a theorem which formally resembles Quillen's Theorem A.

Domaines: Catégories et ensembles [math.CT]; Topologie algébrique [math.AT]

Léonard Guetta. HOMOLOGY OF CATEGORIES VIA POLYGRAPHIC RESOLUTIONS. Journal of Pure and Applied Algebra, 2021, 225 (10). ⟨hal-02512607v3⟩