Definition functorcategoryright_map_laws: psfunctor_laws functorcategoryright_map_data. Proof. repeat split; red; cbn. - intros B B' F. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. apply idpath. - intros B B' F1 F2 F3 β1 β2. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. apply idpath. - intros B B' F. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. cbn. do 2 rewrite id_right; apply pathsinv0, functor_id. - intros B B' F. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. cbn. do 2 rewrite id_right; apply idpath. - intros B1 B2 B3 B4 F1 F2 F3. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. cbn. do 3 rewrite id_left. rewrite id_right. apply pathsinv0, functor_id. - intros B C D F H1 H2 γ. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. cbn. rewrite id_right; apply id_left. - intros B C D F1 F2 H β. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. apply (nat_trans_eq (homset_property _)). intro a. cbn. rewrite id_right; apply id_left. 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.