Regular-epimorphism-monomorphism factorization from kernel pairs
= Regular-epimorphism-monomorphism factorization from kernel pairs
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.