Fundamental Group of Schurian Categories and the Hurewicz Isomorphism

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 \cite{bu1}. 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.

2010 Mathematics Subject Classification: 55Q05 18D20 16E40 16W25 16W50

Keywords and Phrases: Fundamental group, linear category, Schurian category, Hurewicz, Hochschild

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