Section Iso_Mono_Epi.
Context {C : Category} {a b : Obj} (I : a ≃ b).
Program Definition Ismorphism_Monic : a ≫–> b :=
{|
mono_morphism := I
|}.
Next Obligation. (* mono_morphism_monomorphism *)
Program Definition Ismorphism_Epic : b –≫ a :=
{|
mono_morphism := inverse_morphism I
|}.
Next Obligation. (* epi_morphism_epimorphism *)
End Iso_Mono_Epi.

(** If two objects are isomorphic in category C then they are also isomorphic in C^op. *)
Theorem CoIso {C : Category} (a b : C) : a ≃≃ b ::> C → a ≃≃ b ::> C^op.