Bundle functors on fibred manifolds (Q911111)

The theory of bundle functors extends the classical theory of natural bundles and operators to more general categories over manifolds and so generalizes (and unifies) the methods for classification of geometric objects and operations. In this paper, the regularity of bundle functors is proved for certain class of categories over manifolds and classification results including sharp estimates of the orders are obtained for functors on fibred manifolds with fixed dimensions of bases and fibers. Further, bundle functors on the latter categories which preserve the fibred products are described in the terms of Weil algebras. At the end, the author treats some natural operators with vector fields.