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

Lemma another_coequalizer
(c c' : C)
(h : (c' –≻ c)%morphism)
:
((equalizer_morph (Type_Cat_Has_CoEqualizers _ _ (Trans f c') (Trans g c'))) ∘ (B _a h) ∘ (Trans f c))%morphism
=
((equalizer_morph (Type_Cat_Has_CoEqualizers _ _ (Trans f c') (Trans g c'))) ∘ (B _a h) ∘ (Trans g c))%morphism
.