Homology of categories via polygraphic resolutions

Abstract

In this paper, we extend a result of Lafont and M{é}tayer and prove that the polygraphic homology of a small category, defined in terms of polygraphic resolutions in the category $\omega$Cat of strict $\omega$-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.

References in corpus (4)

• Higher Topos Theory
• A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof
• Towards a Thomason model structure on the category of strict n-categories
• A derivability criterion based on the existence of adjunctions