Sheaves of ordered spaces and interval theories
Algebraic Topology
2009-12-21 v2 Category Theory
Abstract
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category turns out to be a certain full subcategory of a topos of sheaves over a simpler site. A precise characterisation of this subcategory is provided. The ambient topos makes available some general homotopical machinery.
Cite
@article{arxiv.0808.1820,
title = {Sheaves of ordered spaces and interval theories},
author = {Krzysztof Worytkiewicz},
journal= {arXiv preprint arXiv:0808.1820},
year = {2009}
}