# Article

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Keywords:
Weil bundle; fiber product preserving bundle functor; action of smooth category
Summary:
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.
References:
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