Homotopic chain maps have equal \(s\)-homology and \(d\)-homology (Q1751468)

Summary: 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 \(n\)th \(d\)-homology \(R\)-modules are isomorphic, and if \(X\) is a contractible space, then its \(n\)th \(d\)-homology \(R\)-modules for \(n \neq 0\) are trivial.