Categories and the Foundations of Classical Field Theories

TL;DR

This paper reviews recent applications of category theory to analyze the structure and equivalence of classical field theories like Newtonian gravitation, general relativity, and Yang-Mills theories.

Contribution

It introduces categorical methods to assess the theoretical structure and equivalence of various classical field theories, offering a new perspective on their foundational relationships.

Findings

Categorical frameworks clarify the structural similarities among classical field theories.

Category theory provides tools to assess theoretical equivalence.

The approach unifies different classical theories under a common formalism.

Abstract

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.