Shape of compacta as extension of weak homotopy of finite spaces

TL;DR

This paper introduces a categorical framework that classifies compact Hausdorff spaces by their shape and finite spaces by their weak homotopy type, bridging shape theory and homotopy theory.

Contribution

It develops a new category that unifies the classification of compact Hausdorff spaces and finite spaces through shape and weak homotopy types.

Findings

A category that classifies compact Hausdorff spaces by shape.

A category that classifies finite spaces by weak homotopy type.

Establishment of a unified framework connecting shape theory and homotopy theory.

Abstract

We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type.