Hypercovers in Differential Geometry
Category Theory
2026-02-13 v1 Differential Geometry
Abstract
In this paper we provide a simple proof that for several sites of interest in differential geometry, the local projective model structure and the \v{C}ech projective model structure are equal. In particular, this applies to the site of smooth manifolds with open covers and the site of cartesian spaces with good open covers. As an application, we show that for a presheaf of sets on these sites, applying the plus construction once is enough to sheafify.
Keywords
Cite
@article{arxiv.2602.11971,
title = {Hypercovers in Differential Geometry},
author = {Cheyne Glass and Emilio Minichiello},
journal= {arXiv preprint arXiv:2602.11971},
year = {2026}
}
Comments
Preprint version, 60 pages, comments welcome!