Section Arrow_Hom_eq_simplify.
Context {a b : Arrow C} (f g : Arrow_Hom a b).

(** Two arrow homomorphisms are equal if the arrows between theor domains and codomain are respectively equal. In other words, we don't care about the proof of the diagram commuting. *)
Lemma Arrow_Hom_eq_simplify : Arr_H f = Arr_H g → Arr_H' f = Arr_H' g → f = g.