Definition groupoidal_to_inv2cells_data (B : bicat) : psfunctor_data (bicat_of_groupoidal B) (bicat_of_inv2cells B). Proof. use make_psfunctor_data. - exact (λ x, pr1 x ,, tt). - exact (λ _ _ f, f). - simple refine (λ x y f g α, pr1 α ,, _). exact (pr2 y (pr1 x) (pr1 f) (pr1 g) (pr1 α)). - refine (λ x, id2 _ ,, _) ; cbn. is_iso. - refine (λ _ _ _ f g, id2 _ ,, _) ; cbn. is_iso. 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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Eso. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.BicatOfInvertibles. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.UniversalArrow.