Each full reflective subcategory X of a finitely-complete category C gives rise to a factorization system (E,M) on C, where E consists of the morphisms of C inverted by the reflexion I : C → X . Under a simplifying assumption which is satisfied in many practical examples, a morphism f : A → B lies in M precisely when it is the pullback along the unit ηB : B → IB of its reflexion If : IA → IB; w...
