On Homology Monoids of Simplicial Abelian Monoids

摘要

The homology semimodules Hn (5) of a presimplicial semimodule S 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 Hn(A) are isomorphic to the homotopy groups π_n(A).