Let ∫: A → B be an R-module homomorphism.

(a) ∫ is a monomorphism if and only if for every pair of R-module homomorphisms g,h: D → A such that ∫g = ∫h, we have g = h. 

(b) ∫ is an epimorphism if and only if for every pair of R-module homomorphisms k,t: B → C such that k∫ = t∫, we have k = t.