Section Comma_Left_Func_Iso_FC_Iso.
Context
{F F' : (B –≻ C)%functor}
(I : (F ≃ F')%natiso)
(G : (D –≻ C)%functor)
.

(** Functors produced from a natural isomorphism and its inverse are inverses. *)
Lemma Comma_Left_Func_Iso_FC_Iso :
((Comma_Left_Func_Iso_FC I G)
∘
(Comma_Left_Func_Iso_FC (Inverse_Isomorphism I) G))%functor
=
Functor_id _
.