Regular epimorphisms are strong epimorphisms
= Regular epimorphisms are strong epimorphisms
The coequalizer universal property supplies the diagonal filler against any <monomorphism>, so every <regular epimorphism> is strong. In a <regular category>, every strong epimorphism is regular: factor it as a regular epimorphism followed by a monomorphism and use the lifting property to make the monomorphism an isomorphism.