Juan Felipe Ruiz Castrillon

A simplified categorical approach to several Galois theories

We discuss the concept of Galois structure and Galois epimorphism in a general setting. Namely, a Galois structure for an epimorphism $π\colon M\to B$ in some category ${\mathcal C}$ is the action of a group object that gives to $M$ the structure of principal homogeneous space in the relative category ${\mathcal C}_B$.