Fiber product preserving bundle functors as modified vertical Weil functors

摘要

We introduce the concept of modified vertical Weil functors on the category of fibred manifolds with m-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors T (A) corresponding to Weil algebras A by the so called modified Weil functors T (A) corresponding to Weil algebra bundle functors A on the category of m-dimensional manifolds and their embeddings.