Product preserving bundle functors on fibered manifolds

We introduce the concept of an involution of iterated bundle functors. Then we study the problem of the existence of an involution for bundle functors defined on the category of fibered manifolds with m-dimensional bases and of fibered manifold morphisms covering local diffeomorphisms. We also apply our results to prolongation of connections.

On the existence of prolongation of connections

Miroslav Doupovec, Włodzimierz M. Mikulski (2006)

Czechoslovak Mathematical Journal

Similarity:

We classify all bundle functors $G$ admitting natural operators transforming connections on a fibered manifold $Y \to M$ into connections on $G Y \to M$ . Then we solve a similar problem for natural operators transforming connections on $Y \to M$ into connections on $G Y \to Y$ .