  A stratified space is a kind of topological space together with a partition
into smooth manifolds. These kinds of spaces naturally arise in the study of
singular algebraic varieties, symplectic reduction, and differentiable stacks.
In this paper, we introduce a particular class of stratified spaces called
stratified vector bundles, and provide an alternate characterization in terms
of monoid actions. We will then provide large families of examples coming from
the theory of Whitney stratified spaces, singular foliation theory, and
equivariant vector bundle theory. Finally, we extend functorial properties of
smooth vector bundles to the stratified case.
