Fiber product preserving bundle functors on all morphisms of fibered manifolds. (English) Zbl 1164.58306

Kolář, Ivan; Mikulski, Włodzimierz M.

Arch. Math., Brno 42, No. 3, 285-293 (2006).

Let \(\mathcal {FM}\) be the category of all fibered manifolds and fibered morphisms. In the paper all fiber product preserving functors on \(\mathcal {FM}\) are described in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of \(r\)-jets by algebra homomorphisms. An explicit formula for the iteration of two such functors is given and the special attention is payed to functors with values in vector bundles.

Reviewer: Josef Janyška (Brno)

MSC:

58A20	Jets in global analysis
58A32	Natural bundles

Keywords:

Weil algebra; \(r\)-jet