Definition all_companions_rel : all_companions_double_cat rel_double_cat. Proof. refine (λ (X Y : hSet) (f : X → Y), _). simple refine (_ ,, _). - exact (λ x y, (f x = y)%logic). - use make_double_cat_are_companions'. + abstract (exact (λ x y p, p)). + abstract (exact (λ x y p, maponpaths f p)). + abstract (repeat (use funextsec ; intro) ; apply propproperty). + abstract (repeat (use funextsec ; intro) ; apply propproperty). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Relations. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Categories.Rel. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. 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.SymmetricUnivalent. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints.