Non-existence of natural operators transforming connections on $Y\to M$ into connections on $FY\to Y$

W. M. Mikulski

Address.
  Institute of Mathematics, Jagiellonian University, Reymonta 4, Krak\'ow, Poland
 

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

Abstract.
Under some weak assumptions on a bundle functor $F:\Cal F\Cal M_{m,n}\to\Cal F\Cal M$ we prove that there is no $\Cal F \Cal M_{m,n}$-natural operator transforming connections on $Y\to M$ into connections on $FY\to Y$.

AMSclassification. 58A32, 58A05, 58A20.

Keywords.  Bundle functors, natural bundles, natural operators, connections.