Homology of categories via polygraphic resolutions

Abstract

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