Definition lax_extension_to_lax_double_functor {V : quantale_cosmos} {F : SET ⟶ SET} (L : lax_extension V F) : lax_double_functor (enriched_rel_univalent_double_cat V) (enriched_rel_univalent_double_cat V). Proof. use make_enriched_relation_lax_double_functor. - exact F. - exact (λ X Y R, L X Y R). - exact (λ X₁ X₂ Y₁ Y₂ R S f g p, lax_extension_enriched_relation_square L p). - exact (lax_extension_id_enriched_relation L). - exact (λ X Y Z R S, lax_extension_enriched_rel_comp L R S). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.EnrichedRels. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor. Require Import UniMath.Bicategories.DoubleCategories.Examples.EnrichedRelDoubleCat. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichedRelation. Require Import UniMath.CategoryTheory.EnrichedCats.LaxExtension.