effective epimorphism

A morphism $e : A \to B$ is an effective epimorphism if the pullback $A \times_B A$ exists and $e$ is the coequalizer of the two projections $p_1,p_2 : A \times_B A \rightrightarrows A$.By the implications below, effective epimorphisms are closely related to strict and regular epimorphisms. Every effective epimorphism is regular and hence strict, and in a category with pullbacks, every strict epimorphism is effective. Thus, in categories with pullbacks, all three mentioned classes of epimorphisms coincide. See also this overview.