Definition predoublecategory_hor_id_comp (C : predoublecategory_ob_mor_data): UU := (∏ c : C, c -h-> c) × (∏ a b c : C, a -h-> b -> b -h-> c -> a -h-> 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.