Section CoEqualizer.
Context (C : Category) {A B : PreSheaf C} (f g : (A –≻ B)%nattrans).

Lemma CoEq_rel_natural
(a b : C)
(h : (b –≻ a)%morphism)
(x y : (B _o)%object a)
(H : CoEq_rel (Trans f a) (Trans g a) x y)
:
CoEq_rel (Trans f b) (Trans g b) (B _a h x)%morphism (B _a h y)%morphism
.