Department of Algebra and Geometry, Faculty of Science, Masaryk University, Janackovo nam. 2a, 602 00 Brno, Czech Republic
We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of $r$-jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.
AMSclassification. 58A20, 58A32.
Keywords. Fiber product preserving bundle functor, Weil algebra, $r$-jet.