Categories of multiplicative functors and Weil’s infinitely near points

Abstract

At the early fifties A. Weil introduced [3] and algebraic approach to the theory of infinitesimal prolongations of smooth manifolds motivated by the theory of jets developed by Ch. Ehresmann on one side and also by the return to Fermat’s methods on the infinitesimal calculus of first order, that makes use of nilpotent infinitesimals.