The homotopy of chain maps on pre-abelian categories is investigated and equality extended d-homologies of homotopic chain maps is established. Singular and simplicial extended d-homology are introduced. If X and Y are same homotopy type, then their n-th singular extended d-homology R-modules are isomorphic. As a special case if X is a contractible space, then its n-th singular extended d-homology R-modules for n ̸= 0 are trivial.
