Definition psfunctor_fib_to_psfunctor_bicat_data : psfunctor_data (fib_slice_bicat C) (psfunctor_bicat (cat_to_bicat (C^op)) bicat_of_univ_cats). Proof. use make_psfunctor_data. - exact (λ P, indexed_cat_to_psfunctor (cleaving_to_indexed_cat (pr1 P) (pr2 P))). - exact (λ P₁ P₂ F, indexed_functor_to_pstrans (cartesian_disp_functor_to_indexed_functor (pr2 P₁) (pr2 P₂) F)). - exact (λ P₁ P₂ F G τ, indexed_nat_trans_to_modification (disp_nat_trans_to_indexed_nat_trans (pr2 P₁) (pr2 P₂) τ)). - exact (λ P, pr1 (psfunctor_id_fib_to_psfunctor_bicat (pr1 P) (pr2 P))). - exact (λ P₁ P₂ P₃ F G, pr1 (psfunctor_comp_fib_to_psfunctor_bicat _ _ _ F G)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategory. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedFunctor. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedTransformation. Require Import UniMath.CategoryTheory.IndexedCategories.FibrationToIndexedCategory. Require Import UniMath.CategoryTheory.IndexedCategories.CartesianToIndexedFunctor. Require Import UniMath.CategoryTheory.IndexedCategories.NatTransToIndexed. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategoryToFibration. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedFunctorToCartesian. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedTransformationToTransformation. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Discreteness. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.DiscreteBicat. Require Import UniMath.Bicategories.Core.Examples.FibSlice. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.PseudoFunctorsIntoCat. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Transformations.Examples.PseudoTransformationIntoCat. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.Modifications.Examples.ModificationIntoCat. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence.