Definition evaluation_pstrans_data: pstrans_data (comp_psfunctor L R) (id_psfunctor CAT). Proof. use make_pstrans_data. - intro A. apply evaluation_functor. - intros A A' F. apply nat_z_iso_to_invertible_2cell. use make_nat_z_iso. + use make_nat_trans. * intro Gb. apply identity. * intros Gb Gb' βg. induction Gb as [G b]. induction Gb' as [G' b']. induction βg as [β g]. simpl in *. rewrite id_left, id_right. apply functor_comp. + intro a. cbn. apply identity_is_z_iso. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.Modifications.Modification. Import Bicat.Notations.