Differential 1-forms on diffeological spaces and diffeological gluing

This paper aims to describe the behavior of diffeological differential 1-forms under the operation of gluing of diffeological spaces along a smooth map (the results obtained actually apply to all k-forms with k>0). In the diffeological context, two constructions regarding diffeological forms are available, that of the vector space Omega^1(X) of all 1-forms, and that of the (pseudo-)bundle Lambda^1(X) of values of 1-forms. We describe the behavior of the former under an arbitrary gluing of two diffeological spaces, while for the latter, we limit ourselves to the case of gluing along a diffeomorphism.