Product preserving bundle functors on fibered manifolds. (English) Zbl 0881.58002

Mikulski, W. M.

Arch. Math., Brno 32, No. 4, 307-316 (1996).

Let \(\mathcal M\) denote the category of smooth finite-dimensional manifolds and their smooth maps, and let \(\mathcal {FM}\) denote its fibred analogue. The main result of the paper is an equivalence between (1) product preserving bundle functors \(F : \mathcal {FM} \to \mathcal {FM}\), up to the natural equivalence of functors, and (2) triples \(\mu ,G,H\) where \(G,H\) are product preserving bundle functors \(\mathcal M \to \mathcal {FM}\) and \(\mu \) is a natural transformation between them, up to the equivalence of natural transformations. The paper ends with a corollary which characterizes vertical Weil bundle functors \(F : \mathcal {FM} \to \mathcal {FM}\).

Reviewer: Michal Marvan (Opava)

MSC:

58A05

Differentiable manifolds, foundations

Keywords:

product preserving bundle functors; natural transformations; Weil bundle functors