# Weilian prolongations of actions of smooth categories

## Ivan Kolář

Address: Institut of Mathematics and Statistics Faculty of Science, Masaryk University Janáčkovo nám. 2a, 602 00 Brno, Czech Republic

E-mail: kolar@math.muni.cz

Abstract: First of all, we find some further properties of the characterization of fiber product preserving bundle functors on the category of all fibered manifolds in terms of an infinite sequence $A$ of Weil algebras and a double sequence $H$ of their homomorphisms from [5]. Then we introduce the concept of Weilian prolongation $W_H^A S$ of a smooth category $S$ over ${\mathbb{N}}$ and of its action $D$. We deduce that the functor $(A,H)$ transforms $D$-bundles into $W_H^AD$-bundles.

AMSclassification: Primary: 58A20; Secondary: 58A32.

Keywords: Weil bundle, fiber product preserving bundle functor, action of smooth category