Grothendieck topologies
The notion of a Grothendieck topology allows the unification of the theory of the fundamental group in topology and Galois theory in field theory. In this video we take a peek at this notion by giving the definition and showing how it provides the data required to give rise to the notion of a sheaf generalising the notion of a sheaf on a topological space. We then look at the Grothendieck topology that is useful for Galois theory and show how the notion of a sheaf here corresponds to a set with a continuous action of the absolute Galois group.