On the category of stratifolds
arXiv:1605.04142
Abstract
Stratifolds are considered from a categorical point of view. We show among others that the category of stratifolds fully faithfully embeds into the category of -algebras as does the category of smooth manifolds. We prove that a variant of the Serre-Swan theorem holds for stratifolds. In particular, the category of vector bundles over a stratifold is shown to be equivalent to the category of vector bundles over an associated affine scheme although the latter is in general larger than the stratifold itself.
20 pages. Final version, to appear in Cahiers de Topologie et Géometrie Differentielle Catégoriques