Homotopic Chain Maps Have Equal s-Homology and d-Homology

الملخص EN

The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and d-homologies of homotopic chain maps is established.

As a special case, if X and Y are the same homotopy type, then their nth d-homology R-modules are isomorphic, and if X is a contractible space, then its nth d-homology R-modules for n≠0 are trivial.