On the structure of étale fibrations of L∞-bundles

We prove that an etale fibration between -bundles admits local sections composed of several elementary morphisms of particularly simple and accessible type. As applications, we establish an inverse function theorem for L infinity-bundles and provide an elementary proof that every weak equivalence of -bundles induces a quasi-isomorphism of the differential graded algebras of global functions. Furthermore, we apply this inverse function theorem to show that the homotopy category of L infinity -bundles admits a simple description in terms of homotopy classes of morphisms, when -bundles are restricted to their germs around their classical loci.