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

(** Two functors are equal if their object maps and arrow maps are. *)
Lemma Functor_eq_simplify (Oeq : F _o = G _o) :
((fun x y =>
match Oeq in _ = V return ((x –≻ y) → ((V x) –≻ (V y)))%morphism with
eq_refl => F  @_a x y
end) = G @_a) -> F = G.