On Equation Manifolds, the Vinogradov Spectral Sequence, and Related Diffeological Structures

We consider basic diffeological structures that can be highlighted naturally within the theory of the Vinogradov spectral sequence and equation manifolds. These interrelated features are presented in a rigorous and accurate way, that complements some heuristic formulations appearing in very recent literature. We also propose a refined definition of the Vinogradov spectral sequence using diffeologies.