Product preserving gauge bundle functors on all principal bundle homomorphisms. (English) Zbl 1219.58001

Mikulski, Włodzimierz M.

Ann. Pol. Math. 101, No. 2, 163-207 (2011).

The author completely describes the product preserving gauge bundle functors (ppgb-functors) on the category \(PB\) of principal bundles and principal bundle homomorphisms and their natural transformations, in terms of admissible triples and their morphisms. It is shown that any ppgb-functor on \(PB\) admits a prolongation of principal connections to general ones, and a “reduction” theorem for prolongations of principal connections into principal ones by means of Weil functors is proved. An appendix which generalizes the results from [W. M. Mikulski, Monatsh. Math. 119, No. 1–2, 63–77 (1995; Zbl 0823.58004)], contains the classification of the natural operators lifting vector-valued 1-forms (or vector-valued maps) to vector-valued 1-forms on Weil bundles.

Reviewer: Vladimir Balan (Bucureşti)

MSC:

58A32	Natural bundles
58A05	Differentiable manifolds, foundations
58A20	Jets in global analysis

Keywords:

natural bundles; gauge bundles; product preserving bundle functors; natural transformations; principal bundles; general connections; principal connections; Weil bundles; Weil algebras

Citations:

Zbl 0823.58004