Submission date: 26 August 2021

Abstract:

We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We will show in future work that its cofibrant objects are precisely the “weak polytopes” of Knebusch.

Mathematics Subject Classification: 55U40 (Primary) 03C64, 18F10, 55U35 (Secondary)

Keywords and phrases:

Full text arXiv 2108.11952: pdf, ps.