## Product preserving gauge bundle functors on all principal bundle homomorphisms

### Volume 101 / 2011

#### Abstract

Let $\mathcal{P}\mathcal{B}$ be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on $\mathcal{P}\mathcal{B}$ and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on $\mathcal{P}\mathcal{B}$ admits a prolongation of principal connections to general ones. We also prove a “reduction” theorem for prolongations of principal connections into principal ones by means of Weil functors. We observe that there exist plenty of such prolongations. In Appendix, we classify the natural operators lifting vector-valued $1$-forms (or vector-valued maps) to vector-valued $1$-forms on Weil bundles.