effective monomorphism

A morphism $m : A \to B$ is an effective monomorphism if the pushout $B \sqcup_A B$ exists and $m$ is the equalizer of the two coprojections $i_1,i_2 : B \rightrightarrows B \sqcup_A B$.By the implications below, effective monomorphisms are closely related to strict and regular monomorphisms. Every effective monomorphism is regular and hence strict, and in a category with pushouts, every strict monomorphism is effective. Thus, in categories with pushouts, all three mentioned classes of monomorphisms coincide. See also this overview.