# Fiber product preserving bundle functors on all morphisms of fibered manifolds

Ivan Kolář; Włodzimierz M. Mikulski

Archivum Mathematicum (2006)

- Volume: 042, Issue: 3, page 285-293
- ISSN: 0044-8753

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topKolář, Ivan, and Mikulski, Włodzimierz M.. "Fiber product preserving bundle functors on all morphisms of fibered manifolds." Archivum Mathematicum 042.3 (2006): 285-293. <http://eudml.org/doc/249781>.

@article{Kolář2006,

abstract = {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.},

author = {Kolář, Ivan, Mikulski, Włodzimierz M.},

journal = {Archivum Mathematicum},

keywords = {fiber product preserving bundle functor; Weil algebra; $r$-jet; Weil algebra; -jet},

language = {eng},

number = {3},

pages = {285-293},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Fiber product preserving bundle functors on all morphisms of fibered manifolds},

url = {http://eudml.org/doc/249781},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Kolář, Ivan

AU - Mikulski, Włodzimierz M.

TI - Fiber product preserving bundle functors on all morphisms of fibered manifolds

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 3

SP - 285

EP - 293

AB - 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.

LA - eng

KW - fiber product preserving bundle functor; Weil algebra; $r$-jet; Weil algebra; -jet

UR - http://eudml.org/doc/249781

ER -

## References

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- Kolář I., Cabras A., On the functorial prolongations of principal bundles, to appear in CMUC. Zbl1150.58002MR2337425
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- Kolář I., Mikulski W. M., On the fiber product preserving bundle functors, Differential Geometry and Its Applications 11 (1999), 105–115. (1999) Zbl0935.58001MR1712139
- Mikulski W. M., There exists a prolongation functor of infinite order, Časopis pěst. mat. 114 (1989), 57–59. (1989) Zbl0672.58002MR0990118
- Mikulski W. M., Natural transformations of Weil functors into bundle functors, Rend. Circ. Mat. Palermo (2), Suppl. 22 (1989), 177–191. (1989) MR1061799
- Weil A., Théorie des points proches sur les variétes différentielles, Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. (1953) MR0061455

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