Sheaves of ordered spaces and interval theories

Details Sheaves of ordered spaces and interval theories Sheaves of ordered spaces and interval theories

2008-08-13

arxiv.org/abs/0808.1820v2

Mathematics

Algebraic Topology

Scientific paper

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.

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