Fundamental group of Schurian categories and the Hurewicz isomorphism

CLAUDE CIBILS; MARIA JULIA REDONDO; ANDREA SOLOTAR

DOCUMENTA MATHEMATICA

UNIV BIELEFELD

Lugar: Bielefeld; Año: 2011 vol. 16 p. 581 - 595

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