Synthetic approach to the Quillen model structure on topological spaces

Ebel, Sterling; Kapulkin, Krzysztof

doi:10.2140/agt.2025.25.1227

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Synthetic approach to the Quillen model structure on topological spaces

Sterling Ebel and Krzysztof Kapulkin

Algebraic & Geometric Topology 25 (2025) 1227–1264

DOI: 10.2140/agt.2025.25.1227

Abstract

We provide an axiomatic treatment of Quillen’s construction of the model structure on topological spaces to make it applicable to a wider range of settings, including $Δ$ -generated spaces and pseudotopological spaces. We use this axiomatization to construct a model structure on the category of locales.

Keywords

model structure, topological spaces, locales, pseudotopological spaces

Mathematical Subject Classification

Primary: 18N40, 55U35

Secondary: 18F70

References

Publication

Received: 22 October 2023

Revised: 13 February 2024

Accepted: 5 March 2024

Published: 16 May 2025

Authors

Sterling Ebel
Department of Mathematics University of Western Ontario London, ON Canada

Krzysztof Kapulkin
Department of Mathematics University of Western Ontario London, ON Canada

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Volume 25, issue 2 (2025)