Definition strict_square_double_cat (C : setcategory) : strict_double_cat. Proof. use make_strict_double_cat. - exact C. - exact (arrow_twosided_disp_cat C). - apply is_strict_arrow_twosided_disp_cat. - exact (hor_id_arrow_twosided_disp_cat C). - exact (hor_comp_arrow_twosided_disp_cat C). - abstract (intros x y f ; cbn ; apply id_left). - abstract (intros x y f ; cbn ; apply id_right). - abstract (intros w x y z f g h ; cbn ; apply assoc). - abstract (intro ; intros ; apply homset_property). - abstract (intro ; intros ; apply homset_property). - abstract (intro ; intros ; apply homset_property). 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.