Fundamental group of Schurian categories and the Hurewicz isomorphism

Details Fundamental group of Schurian categories and the Hurewicz isomorphism Fundamental group of Schurian categories and the Hurewicz isomorphism

2010-10-29

arxiv.org/abs/1010.6296v2

Mathematics

Rings and Algebras

Final version to appear in Documenta Mathematica, 14 pages

Scientific paper

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.

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