Condensed mathematics through compactological spaces
Functional Analysis
2025-12-17 v1 Algebraic Topology
Category Theory
Logic
Abstract
In their 2022 lecture notes on condensed sets, Clausen and Scholze mentioned in a remark that the important subclass of quasiseparated condensed sets is equivalent to the category of so-called compactological spaces defined by Waelbroeck in the 1960s. In this paper we survey the latter category in detail, we give a rigorous proof of Clausen and Scholze's claim, and we establish that condensed sets are a formal categorical completion of Waelbroeck's compactological spaces. The latter answers a question asked by Hanson in 2023 and permits the interpretation of compactological sets as an 'elementary' approach to condensed mathematics.
Cite
@article{arxiv.2512.14612,
title = {Condensed mathematics through compactological spaces},
author = {Franziska Böhnlein and Benjamin Bruske and Sven-Ake Wegner},
journal= {arXiv preprint arXiv:2512.14612},
year = {2025}
}
Comments
34 pages, comments welcome