Geodesic
Weilian prolongations of actions of smooth categories
Archivum mathematicum, Tome 44 (2008) no. 2, pp. 133-138.

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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.
Classification : 58A20, 58A32
Keywords: Weil bundle; fiber product preserving bundle functor; action of smooth category 
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     author = {Kol\'a\v{r}, Ivan},
     title = {Weilian prolongations of actions of smooth categories},
     journal = {Archivum mathematicum},
     pages = {133--138},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2008},
     mrnumber = {2432850},
     zbl = {1212.58001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008__44_2_a5/}
}
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Kolář, Ivan. Weilian prolongations of actions of smooth categories. Archivum mathematicum, Tome 44 (2008) no. 2, pp. 133-138. http://geodesic.mathdoc.fr/item/ARM_2008__44_2_a5/