Functorial prolongations of some functional bundles
  We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. We study the prolongation of vector fields in both cases and we prove that the bracket is preserved. Our proof is based on several new results concerning the finite dimensional Weil bundles. 
Antonella Cabras, Josef Jany\v{s}ka, Ivan Kol\'a\v{r}