M. Doupovec, Department of Mathematics, Brno University of Technology, FSI VUT Brno, Technicka 2, 616 69 Brno, Czech Republic
W. M. Mikulski, Institute of Mathematics, Jagiellonian University, Krakow, Reymonta 4, Poland
Let $F$ be a natural bundle. We introduce the geometrical construction transforming two general connections into a~general connection on the $F$-vertical bundle. Then we determine all natural operators of this type and we generalize the result by I\. Kol\'a\v r and the second author on the prolongation of connections to $F$-vertical bundles. We also present some examples and applications.
Keywords. Connection, vertical bundle.