Definition Cat_data : prebicategory_data. Proof. unfold prebicategory_data. exists Cat_id_comp. repeat split. - intros. simpl in a,b,c,d. exact (Catlike_associator a b c d (univalent_category_has_homsets b) (univalent_category_has_homsets c) (univalent_category_has_homsets d)). - intros. simpl in a, b. exact (Catlike_left_unitor a b (univalent_category_has_homsets a) (univalent_category_has_homsets b)). - intros. simpl in a, b. exact (Catlike_right_unitor a b (univalent_category_has_homsets b)). Defined.
Require Import UniMath.Foundations.PartD. 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory.