THE INTRINSIC FUNDAMENTAL GROUP OF A LINEAR CATEGORY

Claude Cibils (1) , Maria Julia Redondo (2) , Andrea Solotar (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 UNS - Universidad Nacional del Sur [Argentina]
3 Departamento de Matemática [Buenos Aires]

We provide an intrinsic definition of the fundamental group of a li\-near category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.

Mots clés: Fundamental group; quiver; presentation; linear category; Hochschild-Mitchell

Domaines: Anneaux et algèbres [math.RA]; Catégories et ensembles [math.CT]; K-théorie et homologie [math.KT]; Théorie des représentations [math.RT]

Claude Cibils, Maria Julia Redondo, Andrea Solotar. THE INTRINSIC FUNDAMENTAL GROUP OF A LINEAR CATEGORY. Algebras and Representation Theory, 2012, 15 (4), pp.735-753. ⟨10.1007/s10468-010-9263-1⟩. ⟨hal-00155286v4⟩