Definition ε'ntiso : z_iso (C:= [D,D]) (G ∙ F) (functor_identity _ ). Proof. eapply z_iso_comp. set (XR := functor_on_z_iso GG (functor_on_z_iso FF εntiso)). set (XR':= z_iso_inv_from_z_iso XR). apply XR'. eapply z_iso_comp. 2: apply εntiso. set (XR := functor_on_z_iso (pre_comp_functor G) (z_iso_inv_from_z_iso ηntiso)). set (XR':= functor_on_z_iso (post_comp_functor F) XR). apply XR'. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core.