Definition make_lax_double_functor {C₁ C₂ : univalent_double_cat} (F : C₁ ⟶ C₂) (FF : twosided_disp_functor F F (hor_mor C₁) (hor_mor C₂)) (FI : double_functor_hor_id FF (hor_id_double_cat C₁) (hor_id_double_cat C₂)) (FC : double_functor_hor_comp FF (hor_comp_double_cat C₁) (hor_comp_double_cat C₂)) (Fl : double_functor_lunitor (double_cat_double_lunitor C₁) (double_cat_double_lunitor C₂) FI FC) (Fr : double_functor_runitor (double_cat_double_runitor C₁) (double_cat_double_runitor C₂) FI FC) (Fa : double_functor_associator (double_cat_double_associator C₁) (double_cat_double_associator C₂) FC) : lax_double_functor C₁ C₂. Proof. simple refine ((((F ,, FF) ,, _) ,, _) ,, tt). - split ; cbn. + exact FI. + exact FC. - repeat split ; cbn. + exact Fl. + exact Fr. + exact Fa. Defined.
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.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfDispCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfTwoSidedDispCat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleTransformation. Require Import UniMath.Bicategories.DoubleCategories.Core.BicatOfDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats.