From inverse to coherent systems

In a commutative inverse sequence by a natural replacement of spaces with homotopy equivalent spaces an inverse sequence is obtained, which is not commutative. It is proved that the two inverse sequences are isomorphic in the category of strong fundamental sequences. proved that level coherent maps between sequences in the coherent category have a very simple description, i.e., can be considered as strong fundamental sequences. As a corollary it is shown that the two inverse sequences are isomorphic in the coherent category Coh of coherent inverse systems and coherent maps.