## The natural affinors on some fiber product preserving
gauge bundle functors of vector bundles

##
*Jan Kurek and Wlodzimierz M. Mikulski*

**Address.**

Institute of Mathematics,
Maria Curie-Sklodowska University,
Lublin, Pl. Marii Curie-Sklodowskiej 1, Poland

Institute of Mathematics,
Jagellonian University,
Krakow, Reymonta 4, Poland

**E-mail. **kurek@golem.umcs.lublin.pl

**E-mail. **mikulski@im.uj.edu.pl

**Abstract.**

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.