Strong shape in categories enriched over groupoids

For any pair of categories (C, K) enriched over the category Gpd of groupoids, it is possible to define a strong shape category SSh(C, K) in such a way that, for C the category of topological spaces and K its full subcategory of spaces having the homotopy type of absolute neighborhoods retracts for metric spaces, one obtains the strong shape category SSh(Top) , as defined by Mardešić. We also introduce a new category SSK with the same objects as C and morphisms given by suitable pseudo-natural transformations into the category of groupoids. The main result is then that such a category SSK is isomorphic to the strong shape category SSh(C, K) , when C is also a proper model category.