A note on delay-inverse systems, I

A generalization of an inverse system in a category was recently introduced, as well as that of the corresponding pro-category These so called the delay-inverse systems and delay-pro-category could potentially yield a new theory of (delay-) inverse systems as well as a kind of coarser abstract shape theory. However, we have proven that, whenever an indexing set has cardinality ${\mathrm{\aleph }}_n,n\in {\mathbb{N}}_0$, the potential new theory reduces, in its essence (the classification and invariants), to the ordinary one.