## Fiber product preserving bundle functors on all morphisms of fibered
manifolds

*I. Kolar, W. M. Mikulski*

Address.

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

**E-mail.** kolar@math.muni.cz mikulski@im.uj.edu.pl

**Abstract****.**

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.