Definition disp_cat_id_comp (C : precategory_data) (D : disp_cat_ob_mor C) : UU := (forall (x:C) (xx : D x), xx -->[identity x] xx) × (forall (x y z : C) (f : x --> y) (g : y --> z) (xx:D x) (yy:D y) (zz:D z), (xx -->[f] yy) -> (yy -->[g] zz) -> (xx -->[f · g] zz)).
Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering.