On Whitehead's theorem beyond pointed connected spaces

TL;DR

This paper extends Whitehead's theorem to the 2-category of all spaces, not just pointed connected ones, by demonstrating that tori form a strong generator.

Contribution

It shows that the 2-category of spaces admits a strong generator of tori, generalizing Whitehead's theorem beyond pointed connected spaces.

Findings

Whitehead's theorem holds for the 2-category of all spaces.

Tori form a strong generator in this 2-category.

The result applies to spaces that are not necessarily connected or pointed.

Abstract

We prove that the 2-category of spaces admits a strong generator made up of the tori. In other words, Whitehead's theorem holds for the 2-category of (not necessarily connected, not pointed) spaces.