The homology semimodules H_n(S) of a presimplicial semimodule S introduced in our earlier paper, are studied in the case where S is a simplicial abelian monoid. In particular, it is shown that if a simplicial abelian monoid A satisfies the Kan condition and the monoid of path components of A is a group, then the homology monoids H_n(A) are isomorphic to the homotopy groups π_n(A).