A Categorical Model for the Hopf Fibration

TL;DR

This paper models the Hopf fibration using small categories, providing a categorical perspective on the topological spaces involved and describing the Hopf map as a functor realization.

Contribution

It introduces a categorical framework for representing the Hopf fibration, linking topological spaces to classifying spaces of small categories.

Findings

Models $S^3$ and $S^2$ as classifying spaces of small categories

Describes the Hopf map as a functor between these categories

Provides a categorical perspective on the Hopf fibration

Abstract

We give a description up to homeomorphism of $S^3$ and $S^2$ as classifying spaces of small categories, such that the Hopf map $S^3\to{}S^2$ is the realization of a functor.