  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. 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.
