Fundamental group of Schurian categories and the Hurewicz isomorphism.

CIBILS, CLAUDE; REDONDO, MARIA JULIA; SOLOTAR, ANDREA

DOCUMENTA MATHEMATICA

UNIV BIELEFELD

Año: 2011 vol. 16 p. 581 - 595

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.