Condensed Sets on Compact Hausdorff Spaces

TL;DR

This paper establishes an equivalence between condensed sets and sheaves on compact Hausdorff spaces, and demonstrates a model structure on the category of condensed sets, advancing the understanding of their categorical and topological properties.

Contribution

It proves the equivalence of condensed sets with sheaves on compact Hausdorff spaces and introduces a model structure on their category, providing new insights into their mathematical framework.

Findings

Condensed sets are equivalent to sheaves on compact Hausdorff spaces.

A model structure on the category of condensed sets is constructed.

The results deepen the understanding of sheaf-theoretic and topological properties of condensed sets.

Abstract

A condensed set is a sheaf on the site of Stone spaces and continuous maps. We prove that condensed sets are equivalent to sheaves on the site of compact Hausdorff spaces and continuous maps. As an application, we show that there exists a model structure on the category of condensed sets.