Iteration of fiber product preserving bundle functors. (English) Zbl 0999.58001

Doupovec, Miroslav; Kolář, Ivan

Monatsh. Math. 134, No. 1, 39-50 (2001).

After collecting some important facts from the theory of principal prolongations of principal bundles and jet prolongations of associated bundles, the authors consider an arbitrary fiber product preserving bundle functor \(F\) of \({\mathcal FM}_m\) and study the \(F\)-prolongations of principal bundles and of their associated bundles. Then, using the theory of Weil algebras, is described the composition of two product preserving bundle functors on the category of fibered manifolds with \(m\)-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. As applications, are determined certain interesting geometric properties of the natural transformations of some of the iterated functors.

Reviewer: Vladimir Balan (Bucureşti)

MSC:

58A05	Differentiable manifolds, foundations
58A20	Jets in global analysis

Keywords:

Weil algebra; fiber product; bundle functor; Weil bundle; jet bundle; natural transformation