The unification of Mathematics via Topos Theory

TL;DR

This paper proposes a unifying framework for Mathematics using topos theory, viewing Grothendieck toposes as bridges that connect and transfer ideas across different mathematical theories.

Contribution

It introduces a new perspective on Grothendieck toposes as unifying spaces, providing foundational principles for a comprehensive unification of mathematical theories.

Findings

Topos theory can serve as a unifying framework for Mathematics.

Grothendieck toposes act as bridges for transferring mathematical information.

The proposed principles lay groundwork for a unified mathematical foundation.

Abstract

We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for transferring information, ideas and results between distinct mathematical theories.