As some of the above examples show, the property of being an epimorphism is not determined by the morphism alone, but also by the category of context. If D is a subcategory of C, then every morphism in D that is an epimorphism when considered as a morphism in C is also an epimorphism in D. However the converse need not hold; the smaller category can (and often will) have more epimorphisms.
As some of the abov,e examples show, the property of being an epimorphism is not determined by the morphism :alone, but also by the category of context. If D is a subcatego?ry of C, then every morphism in D that is an epimorphism when considered as a morphism in C is also an epimorphism in D. However the converse need not hold; the smaller category can (and often will) have more epimorphisms.