Definition und_ver_cat (C: doublecategory) : category. Proof. use (make_category (und_ver_precategory C)). intros x y. use isaset_total2. - apply C. - intro. use isaset_total2. + apply C. + intro. apply C. Defined.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.