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.