Category Theory and Galois Theory Category Theory and Galois Theory

Abstract. Galois theory translates questions about fields into questions about groups. The fundamental theorem of Galois theory states that there is a bijection between the intermediate fields of a field extension and the subgroups of the corresponding Galois group. After a basic introduction to category and Galois theory, this project recasts the fundamental theorem of Galois theory using categorical language and illustrates this theorem and the structure it preserves through an example. Acknowledgements: I would like to sincerely thank Professor Thomas Fiore for his continual support, encouragement, and invaluable guidance throughout this entire project