Abstract
A covariant functor has been defined in [1] which assigns to a commutative ring R an abelian monoid m(R). The elements of m(R) are equivalence classes (called homotopy classes) of homomorphisms of progenerator modules over R. The monoid homomorphism m(σ): m(R) → m(S) associated with a homomor-phism of rings σ: R → S is studied. Both necessary conditions and sufficient conditions for m(σ)1 {1} = {1}, for m(σ) to be injective and for m(σ) to be surjective are presented.
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