We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
We present a generalization of the concept of semiholonomic jets within the framework of higher order prolongations of a fibred manifold. In this respect, a compilation of our 2-fibred manifold approach with the methods of natural operators theory is used.