Definition two_cat_square_double_cat (C : two_cat) : double_cat. Proof. use make_double_cat. - exact C. - exact (two_cat_arrow_twosided_disp_cat C). - exact (hor_id_two_cat_arrow_twosided_disp_cat C). - exact (hor_comp_two_cat_arrow_twosided_disp_cat C). - exact (double_cat_lunitor_two_cat_arrow_twosided_disp_cat C). - exact (double_cat_runitor_two_cat_arrow_twosided_disp_cat C). - exact (double_cat_associator_two_cat_arrow_twosided_disp_cat C). - exact (triangle_law_two_cat_arrow_twosided_disp_cat C). - exact (pentagon_law_two_cat_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.Core.TwoCategories. Import TwoCategories.Notations. 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.SquaresTwoCat. 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.PseudoDoubleSetCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints.