Cartan's proof for the Darboux theorem in A-modules

Abstract

We refer to [4] for a proof of the (affine) Darboux theorem in the category A-Mod _X of A-modules, defined on a fixed topological space X. Hereby, we present another proof of the same theorem, based on E. Cartan's approach, keeping, as is done in [4], the condition affixed to the coefficient algebra sheaf A, that is, A satisfies the inverse-closed section condition.