The talk will present an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts : this unifies and generalises Grothendieck's theory of ‘Galoisian categories’ and Fraïssé's construction in model theory.

This theory allows one to construct fundamental groups in many classical contexts such as finite groups, finite graphs, motives and many more.

We will in particular present an approach based on it for investigating the independence from l of l-adic cohomology.