Definition reindexing_actegories_disp_psfunctor : disp_psfunctor dBV dBW (id_psfunctor _). Proof. use make_disp_psfunctor. - apply actbicat_disp_2cells_isaprop. - apply actbicat_disp_locally_groupoid. - intros C Act. exact (reindexed_actegory Mon_V Act Mon_W U). - intros C D H ActC ActD ll. exact (reindexed_lax_lineator Mon_V Mon_W U ActC ActD ll). - intros C D H K ξ ActC ActD Hl Kl islntξ. apply preserves_linearity_reindexed_lax_lineator. exact islntξ. - abstract (intros C ActC w c; cbn; rewrite (bifunctor_leftid (actegory_action _ ActC)); do 2 rewrite id_left; apply idpath). - abstract (intros C D E H K ActC ActD ActE Hl Kl w c; cbn; rewrite (bifunctor_leftid (actegory_action _ ActE)) ; rewrite id_left, id_right; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegoryMorphisms. 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.Examples.Identity. Require Import UniMath.Bicategories.MonoidalCategories.BicatOfActegories. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispBuilders. Section PseudofunctorFromReindexing. End PseudofunctorFromReindexing.