Institute of Mathematics, Maria Curie-Sklodowska University, Lublin, Pl. Marii Curie-Sklodowskiej 1, Poland
Institute of Mathematics, Jagellonian University, Krakow, Reymonta 4, Poland
We classify all natural affinors on vertical fiber product preserving gauge bundle functors $F$ on vector bundles. We explain this result for some more known such $F$. We present some applications. We remark a similar classification of all natural affinors on the gauge bundle functor $F^*$ dual to $F$ as above. We study also a similar problem for some (not all) not vertical fiber product preserving gauge bundle functors on vector bundles.
AMSclassification. 58A05, 58A20.
Keywords. Gauge bundle functors, natural operators, natural transformations, natural affinors, jets.