Fiber product preserving  bundle functors on all morphisms of fibered manifolds

I. Kolar, W. M. Mikulski

Department of Algebra and Geometry, Faculty of Science, Masaryk University, Janackovo nam. 2a, 602 00 Brno, Czech Republic

Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60-965 Poznan, Poland


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.