Definition square_double_cat (C : category) : double_cat. Proof. use make_double_cat. - exact C. - exact (arrow_twosided_disp_cat C). - exact (hor_id_arrow_twosided_disp_cat C). - exact (hor_comp_arrow_twosided_disp_cat C). - exact (double_cat_lunitor_arrow_twosided_disp_cat C). - exact (double_cat_runitor_arrow_twosided_disp_cat C). - exact (double_cat_associator_arrow_twosided_disp_cat C). - exact (triangle_law_arrow_twosided_disp_cat C). - exact (pentagon_law_arrow_twosided_disp_cat C). 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.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Arrow. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics. 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.StrictDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints.