The unification of Mathematics via Topos Theory - Russian version

TL;DR

This paper proposes a unifying framework for mathematics using Grothendieck toposes as bridges to connect different mathematical theories, aiming to establish a foundational unification.

Contribution

It introduces a new perspective on topos theory as a foundational tool for unifying diverse mathematical theories and transferring knowledge between them.

Findings

Topos theory can serve as a unifying space for mathematics.

Principles for using toposes as bridges between theories.

Potential for a cohesive foundational framework.

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.