Frölicher Structures, Diffieties, and a Formal Kp Hierarchy

We propose a definition of a diffiety based on the theory of Frolicher structures. As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existence of a suitable derivation on a given diffiety, we can form on it a Kadomtsev-Petviashvili hierarchy which is well-posed. © 2023 American Mathematical Society.