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.
@article{116930,
author = {Ivan Kol\'a\v r},
title = {Weilian prolongations of actions of smooth categories},
journal = {Archivum Mathematicum},
volume = {044},
year = {2008},
pages = {133-138},
zbl = {1212.58001},
mrnumber = {2432850},
language = {en},
url = {http://dml.mathdoc.fr/item/116930}
}
Kolář, Ivan. Weilian prolongations of actions of smooth categories. Archivum Mathematicum, Tome 044 (2008) pp. 133-138. http://gdmltest.u-ga.fr/item/116930/
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