Fundamental group of Schurian categories and the Hurewicz isomorphism

Abstract

Let $k$ be a field. We attach a CW-complex to any Schurian $k$-category and we prove that the fundamental group of this CW-complex is isomorphic to the intrinsic fundamental group of the $k$-category. This extends previous results by J.C. Bustamante in citebu1. We also prove that the Hurewicz morphism from the vector space of abelian characters of the fundamental group to the first Hochschild-Mitchell cohomology vector space of the category is an isomorphism.