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Sheaves of ordered spaces and interval theories

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Krzysztof Worytkiewicz

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. The ambient topos makes available some general
homotopical machinery.

Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, pp. 37-61