Groupoids and strong shape

Ordinary shape equivalences can be defined in full generality, for every pair ( C , K ) of abstract categories. In this paper we consider pairs ( C , K ) enriched over the category of groupoids and show how it is possible, in such a setting, to introduce a general concept of strong shape equivalence. A category Σ ( C , K ) , having the same objects as C , and a functor σ : C → Σ ( C , K ) are defined, so that σ inverts exactly the class of strong shape equivalences.