A Serre–Swan theorem for coisotropic algebras

Coisotropic algebras are used to formalize coisotropic reduction in Poisson geometry as well deformation quantization and find applications various other fields well. In this paper we prove a Serre-Swan Theorem relating the regular projective modules over algebra built out of manifold $M$, submanifold $C$ an integrable smooth distribution $D \subseteq TC$ with vector bundles geometric situation show equivalence categories for case simple distribution.