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Keywords:
Weil bundle; fiber product preserving bundle functor; action of smooth category
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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[4] Kolář, I., Mikulski, W. M.: On the fiber product preserving bundle functors. Differential Geom. Appl. 11 (1999), 105–115. DOI 10.1016/S0926-2245(99)00022-4 | MR 1712139
[5] Kolář, I., Mikulski, W. M.: Fiber product preserving bundle functors on all morphisms of fibered manifolds. Arch. Math. (Brno) 42 (2006), 285–293. MR 2260388 | Zbl 1164.58306
[6] Weil, A.: Théorie des points proches sur les variétés différentielles. Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. MR 0061455
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