Section Functor_eq.
Context {C C' : Category} (F G : (C –≻ C')%functor).

Lemma Functor_eq_morph (H : F = G) :
∃ (H : ∀ x, F _o x = G _o x),
∀ x y (h : (x –≻ y)%morphism),
match H x in _ = V return (V –≻ _)%morphism with
eq_refl =>
match H y in _ = V return (_ –≻ V)%morphism with
eq_refl => F _a h
end
end = G _a h.