Group homomorphism Group monomorphism Let be a group homomorphism. The following statements are equivalent: #m/thm/group is injective; is monic; Proof is injective iff iff iff . Clearly injective implies monic . Now let be a monomorphism. Let be the canonical injection and be the trivial homomorphism. Since , and hence . #state/tidy | #lang/en | #SemBr