Definition functorcategoryright_map_data: psfunctor_data CAT CAT. Proof. use make_psfunctor_data. - exact (fun B => functor_category (pr1 A0) B). - intros B B' F. cbn. exact (post_composition_functor A0 B B' F). - intros B1 B2 F F' β. use make_nat_trans. + intro G. cbn. exact (pre_whisker (pr1 G) β). + intros G G' α. cbn. etrans. 2: { apply horcomp_pre_post. } apply pathsinv0. apply horcomp_post_pre. - intro B. use make_nat_trans. + intro G. cbn. apply ρ_functors_inv. + intros G G' α. apply (nat_trans_eq (homset_property _)). intro a. cbn. rewrite id_left; apply id_right. - intros B1 B2 B3 H F. cbn. use make_nat_trans. + intro G. cbn. apply α_functors. + intros G G' α. cbn. apply (nat_trans_eq (homset_property _)). intro a. cbn. rewrite id_left; apply id_right. 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.