Axiomatic Method and Category Theory

TL;DR

This paper discusses a new axiomatic approach based on category theory, exemplified by Lawvere and Voevodsky, which extends traditional methods and offers novel applications in physics and sciences.

Contribution

It introduces a modern axiomatic framework rooted in categorical logic, expanding the scope of the Axiomatic Method beyond classical foundations.

Findings

Axiomatic approach based on topos and homotopy theories

Potential applications of categorical logic in physics

Extension of the Axiomatic Method beyond classical mathematics

Abstract

Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this method in physics and other natural sciences.