  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 ${\mathbb R}$-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.
