Geodesic
Fundamental group of Schurian categories and the Hurewicz isomorphism
Documenta mathematica, Tome 16 (2011), pp. 581-595.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 citebu1. 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.
Classification : 55Q05, 18D20, 16E40, 16W25, 16W50
Keywords: fundamental group, linear category, Schurian category, Hurewicz, Hochschild 
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     author = {Cibils, Claude and Redondo, Mar{\'\i}a Julia and Solotar, Andrea},
     title = {Fundamental group of {Schurian} categories and the {Hurewicz} isomorphism},
     journal = {Documenta mathematica},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a15/}
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Cibils, Claude; Redondo, María Julia; Solotar, Andrea. Fundamental group of Schurian categories and the Hurewicz isomorphism. Documenta mathematica, Tome 16 (2011), pp. 581-595. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a15/