Coverings and Descent Theory of Finite Spaces

Mbewu, Thomas

Coverings and Descent Theory of Finite Spaces

Master Thesis

2022

Abstract

This thesis presents the categorical Galois theory of the reflection of the category of finite topological spaces into the category of discrete finite topological spaces. This turns out to be nothing but the equivalence between the category of coverings of a connected finite topological space and the actions of the fundamental group of that space. Since some descent theory is necessary for categorical Galois theory, this thesis also contains an account of some of the descent theory of finite topological spaces. The reader is assumed to know the basics of category theory, but no descent theory or categorical Galois theory, or even internal category theory, but to be somewhat familiar with coverings and fundamental groups, and the notion of “locally” for topological spaces.

Keywords

Mathematics and Applied Mathematics

Reference:

Collections

Masters

Full item page