The fundamental group of a linear category

CIBILS, CLAUDE; MARIA JULIA REDONDO; SOLOTAR, ANDREA

Sherbrooke

Conferencia; Conference on Surfaces and Representations; 2010

We provide an intrinsic definition of the fundamental group of a linear 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.