Address. Antonella Cabras, Dipartamento di Matematica Applicata ``G. Sansone",
Via S. Marta 3, 50139 Firenze, Italy
I. Kolar, Department of Algebra and Geometry, Faculty of Science, Masaryk University,
Janackovo nam. 2a, 662 95 Brno, Czech Republic
Abstract. First we deduce some general properties
of product preserving
bundle functors on the category of fibered manifolds. Then we
study the prolongation of projectable tangent valued forms with
respect to these functors and describe the complete lift of the
Fr\"olicher-Nijenhuis bracket. We also present the coordinate
formula for composition of semiholonomic jets.
AMSclassification. 53C05, 58A20.
Keywords. Projectable tangent valued form, product preserving bundle functor, jet, Weil bundle, Fr\"olicher-Nijenhuis bracket.