Abstract. For some Weil algebras $A$, we present a simple procedure giving all natural $T$-functions on the cotangent bundle of a Weil bundle $T^*T^A$. For some other cases, we describe the additional natural functions. We outline the relations of this problem to the problem of lifting of vector fields to the cotangent bundle of a Weil bundle.
AMSclassification. 58A20, 53A55
Keywords. Natural bundle, natural operator, vector field, Weil bundle