Strong n-shape theory

Let μn+1 be the (n+1)-dimensional universal Menger compactum. It is known that the n-shape category of Z-sets in μn+1 is isomorphic to the weak proper n-homotopy category of their complements. In this paper, we introduce the (n+1)-skeletal conic telescope to define the strong n-shape category of compacta, and show that the strong n-shape category of Z-sets in μn+1 is isomorphic to the proper n-homotopy category of their complements.