Product  preserving  bundle  functors  on  manifolds  still  called Weil  functors  were classified  by  [1].  Indeed this author has shown in particular that the set of equivalence classes of such functors are in bijection with the set of equivalence classes of Weil algebras. These functors were used by many authors (ex. [2-4]) to present some lifts of various geometric objects (smooth   functions,   tensor   fields,   linear   connections   on manifolds,...)

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