On the n-movability of maps

This paper continues the study of some movability and co-movability properties for shape morphisms and maps introduced by the authors in [9]. For such morphisms the properties of movability and co-movability with respect to a subcategory are introduced. In particular the properties of n-movability and n-co-movability for maps are defined and studied. As applications, some implications of these properties on the homology and homotopy pro-groups and shape groups are proved.