Geodesic
Fiber product preserving bundle functors on all morphisms of fibered manifolds
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 285-293.

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We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of $r$-jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.
Classification : 58A20, 58A32
Keywords: fiber product preserving bundle functor; Weil algebra; $r$-jet 
@article{ARM_2006__42_3_a10,
     author = {Kol\'a\v{r}, Ivan and Mikulski, W{\l}odzimierz M.},
     title = {Fiber product preserving bundle functors on all morphisms of fibered manifolds},
     journal = {Archivum mathematicum},
     pages = {285--293},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2006},
     mrnumber = {2260388},
     zbl = {1164.58306},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a10/}
}
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Kolář, Ivan; Mikulski, Włodzimierz M. Fiber product preserving bundle functors on all morphisms of fibered manifolds. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 285-293. http://geodesic.mathdoc.fr/item/ARM_2006__42_3_a10/