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Suppose $\mathcal{C}$ is balanced and every morphism of $\mathcal{D}$ factors as a strong epimorphism followed by a monomorphism. For $F:\mathcal{C}\rightleftarrows \mathcal{D}:G$, both unit and counit are pointwise monic exactly when $F$ is full and faithful and its essential image is closed under strong quotients.

A regular epimorphism is a morphism that is the coequalizer of some parallel pair. Every regular epimorphism is a strong epimorphism.

Suppose a category has pullbacks and coequalizers and every pullback of a regular epimorphism is epic. Coequalizing the kernel pair of any morphism produces a factorization as a regular epimorphism followed by a monomorphism. Consequently every strong epimorphism is regular.

A strong quotient of an object $A$ is the codomain of a strong epimorphism out of $A$. A class of objects is closed under strong quotients when every such codomain remains in the class up to isomorphism.