Groupoids and Shape
by
Luciano Stramaccia
Universita' di Perugia - Italia

Shape and Strong Shape are both topological theories of approximation. Ordinary Shape has produced a purely categorical theory with many important results that also better clarify the foundations of the topological theory itself. Although strong shape is by now a well settled theory, the same is not with it, probably because of its intrinsic more geometrical nature.
We present an attempt for a categorical approach to strong shape based on the theory of groupoid-enriched categories. Such (2-)categories have in fact a germ of homotopy in their own structure and we feel that they could deserve for a possible categorization of strong shape and also to obtain some more insights into the structure of the theory. In particular, in our contest, strong shape equivalences have a very nice characterization both in the topological case and in the very general (categorical) setting.

Date received: August 19, 2002