On the category of stratifolds
Category Theory
2017-03-23 v3 Algebraic Geometry
Algebraic Topology
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1605.04142,
title = {On the category of stratifolds},
author = {Toshiki Aoki and Katsuhiko Kuribayashi},
journal= {arXiv preprint arXiv:1605.04142},
year = {2017}
}
Comments
20 pages. Final version, to appear in Cahiers de Topologie et G\'eometrie Differentielle Cat\'egoriques