Lemma is_precategory_cat_of_elems_data : is_precategory cat_of_elems_data. Proof. split; [split|split]; intros; apply cat_of_elems_mor_eq. + apply id_left. + apply id_right. + apply assoc. + apply assoc'. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf.