Weil bundles and jet spaces
Weil prolongations of Banach manifolds in an analytic model of
Weilian prolongations of actions of smooth categories
First of all, we find some further properties of the characterization of fiber product preserving bundle functors on the category of all fibered manifolds in terms of an infinite sequence of Weil algebras and a double sequence of their homomorphisms from [5]. Then we introduce the concept of Weilian prolongation of a smooth category over and of its action . We deduce that the functor transforms -bundles into -bundles.