Constructions of Galois Categories

Abstract

Alexandre Grothendieck, through his groundbreaking work in the 1960s, helped bring algebraic geometry into the modern era. Among his vast work from this period, there is the notion of a Galois category - an example of one being the category of finite etale covers of a scheme. In this thesis we shall investigate Galois categories from a purely categorical perspective and construct examples. In particular, we investigate what it means to be a covering of an object and when such objects form a Galois category.