= Left-exact reflective subcategory of a regular category
Every <left-exact reflective subcategory> of a regular category is regular. The reflector sends a regular-epimorphism--monomorphism factorization to such a factorization among fixed objects. A morphism between fixed objects is a regular epimorphism precisely when the closure of its image under the <closure operation induced by a left-exact reflector> is the whole codomain; pullback stability follows from pullback stability of images and of closure.
Back to article page
