Definition predoublecategory_ver_id_comp (C : predoublecategory_hor) : UU := (∏ c : C, c -v-> c) × (∏ a b c : C, a -v-> b -> b -v-> c -> a -v-> c).
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.