Section Type_Cat_characteristic_function_unique.
Context {A B : Type} (F : @Monic Type_Cat A B) (h : B → Prop)
(hpb : is_PullBack (mono_morphism F) (fun _ => tt) h (fun _ => True)).

Theorem Type_Cat_characteristic_function_unique :
h = fun x => (exists y : A, (mono_morphism F) y = x).