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

Given a Weil algebra A, the concept of A-admissible systems ? is introduced. The complete description is given of the Weil like functors (i.e. product preserving gauge bundle functors) F on the category of triple vector bundles in terms of the AF-admissible systems ?F . Given a Weil like functor 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.