Differential forms on manifolds with boundary and corners

We identify the category of manifolds with boundary and corners with a subcategory of the category {Diffeology}. Then, we show that any differential form on a manifold with boundary or corners, embedded in a smooth manifold, extends to a differential form on an open neighbourhood. As an example of application, we discuss the structure of SO(2)(2) invariant closed 2-forms on R-2n. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.