The fundamental group of a linear category

REDONDO, MARIA JULIA

Curitiba

Congreso; Escuela CIMPA: Algebraic and Geometric aspects of Representation Theory; 2013

Universidad Federal do Parana

In this talk we will present 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, one can prove that this group is isomorphic to the Galois group of the universal covering. We will discuss the behaviour of coverings of  linear categories through fibre products and find a criterion for a covering to be Galois or universal. Finally, we will consider the category of all connected gradings of a linear category by a group G and we show the relation between gradings and Galois coverings. This theoretical tool gives information about the fundamental group of the category and allows us to compute it using complete lists of gradings.