Coherent homotopy of sequences

Abstract

This section is devoted to coherent homotopy of inverse sequences (also called towers) and is not needed in the remaining part of Chapter I. Restriction to inverse sequences greatly simplifies the theory, because in this case the use of homotopies of orders higher than 2 can be avoided. On the other hand, inverse sequences suffice to develop strong shape theory of metric compact, which is the most useful part of strong shape theory. In the introductory subsection, we define coherent homotopy theories, which use homotopies up to a given finite order r ≥ O. However, in the subsection which follows, we use only the case r = 1.