Definition ps_base_ACTI : Base.ps_base ACTI ACTI ⟦ pr111 (Identity.id_psfunctor ACTI), pr111 (Composition.comp_psfunctor acat_to_acti acti_to_acat) ⟧. Proof. intro. exists (functor_identity _). use tpair. + use make_nat_trans. * intro. exists (λ _, identity _). abstract ( intro ; intros ; rewrite id_left ; apply id_right ). * intro ; intros ; use nat_trans_eq. { apply homset_property. } intro ; cbn; rewrite id_left; apply id_right. + use tpair. * use nat_trans_eq. { apply homset_property. } abstract ( intro ; cbn ; rewrite ! id_left ; apply id_right ). * intro ; intro. use nat_trans_eq. { apply homset_property. } abstract ( intro ; cbn ; rewrite ! id_left ; rewrite ! id_right ; rewrite (functor_id ((pr12 x) w)) ; 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.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. 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.Bicategories.MonoidalCategories.BicatOfActegories. Require Import UniMath.Bicategories.MonoidalCategories.BicatOfActionsInBicat. Require Import UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Import BifunctorNotations. Section ActegoryFromObject. End ActegoryFromObject. Section FromActegoriesToActionsInCat. Import MonoidalNotations. End FromActegoriesToActionsInCat. Section FromActionInCatToActegories. End FromActionInCatToActegories.