Strong epimorphism in the category of small categories
= Strong epimorphism in the category of small categories
A functor between small categories is a strong epimorphism precisely when its image generates its codomain as a subcategory. It is a <regular epimorphism> precisely when it is surjective on objects and full. Hence a functor can be strong without being regular when its image arrows generate additional composites that have no single preimage.