Every coequalizer is an epimorphism, a consequence of the uniqueness requirement in the definition of coequalizers. It follows in particular that every cokernel is an epimorphism. The converse, namely that every epimorphism be a coequalizer, is not true in all categories.
Every coequalizer is an epimorphism a consequence of the uniqueness requirement in the definition of coequalizers It follows in particular that every cokernel is an epimorphism The converse namely that every epimorphism be a coequalizer is not true in all categories