Definition objects_of_grpd_data : psfunctor_data grpds one_types. Proof. use make_psfunctor_data. - refine (λ G, make_one_type _ (univalent_category_has_groupoid_ob _)). apply G. - exact (λ _ _ F x, (pr1 F : _ ⟶ _) x). - intros G₁ G₂ F₁ F₂ α ; simpl. intro x. apply isotoid. { apply (pr1 G₂). } use make_z_iso'. + exact ((pr1 α : _ ⟹ _) x). + exact (pr2 G₂ _ _ ((pr1 α : _ ⟹ _) x)). - exact (λ _ _, idpath _). - exact (λ _ _ _ _ _ _, idpath _). 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.Base. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map1Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.Map2Cells. Require Import UniMath.Bicategories.PseudoFunctors.Display.StrictIdentitor. Require Import UniMath.Bicategories.PseudoFunctors.Display.StrictCompositor. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Transformations.Examples.Whiskering. Require Import UniMath.Bicategories.Transformations.Examples.Unitality. Require Import UniMath.Bicategories.Transformations.Examples.Associativity. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.Core.Examples.OneTypes. Require Import UniMath.Bicategories.Core.Examples.Groupoids. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats.