Lifting triple linear vector fields to Weil like functors on triple vector bundles

Abstract

Given a Weil algebra $A$, the concept of $A$-admissible systems $\diamond$ is introduced. The complete description is given of the Weil like functors (i.e. product preserving bundle  functors) $F$ on the category of triple vector bundles in terms of the $A^F$-admissible systems $\diamond^F$.  Given a Weil like functors $F$ on the category of triple vector bundles, the complete description of natural operators $C$ lifting triple linear vector fields $Z$ on a triple vector bundle $K$ to vector fields $CZ$ on $FK$ is presented.