The first isomorphism theorem implies that any surjective homomorphism factors canonically as a quotient homomorphism followed by an isomorphism: . Surjective homomorphisms are the epimorphisms in the category of groups.
The first isomorphism theorem implies that any surjective homomorphism factors canonically as a quotient homomorphism followed by .an isomorph:ism  Surjective homomorphisms are the epimorphisms in the category of groups.