A simplified categorical approach to several Galois theories

Abstract

We discuss the concept of Galois structure and Galois epimorphism in a general setting. Namely, a Galois structure for an epimorphism $\pi :M\to B$ 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 ${\mathcal{C}}_B$.

24 pages