Categorical Foundations for Physics - I: Program at a Glance

TL;DR

This paper explores how category theory-based measures and relations can underpin the laws of physics, providing a structural framework that is independent of specific mathematical representations of physical systems.

Contribution

It introduces a categorical framework for formulating physical laws that are independent of the mathematical structures used to represent physical objects.

Findings

Relations derived from measures in category theory can model physical laws.

The framework supports a theory of the physical entirety.

Relations are independent of specific mathematical structures.

Abstract

Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of mathematical structure that we may represent a physical body or a system of reference with, are, precisely, demanded to be the Laws of Physics by the General Principle of Relativity. This framework leads to a theory for the physical entirety.