Definition cat_prebicat_data : prebicat_data. Proof. use build_prebicat_data. - exact univalent_category. - exact (λ C D, functor C D). - exact (λ _ _ F G, nat_trans F G). - exact (λ C, functor_identity C). - exact (λ _ _ _ F G, functor_composite F G). - exact (λ _ _ F, nat_trans_id F). - exact (λ _ _ _ _ _ α β, nat_trans_comp _ _ _ α β). - exact (λ _ _ _ F _ _ α, pre_whisker F α). - exact (λ _ _ _ _ _ H α, post_whisker α H). - exact (λ _ _ F, nat_trans_id F). - exact (λ _ _ F, nat_trans_id F). - exact (λ _ _ F, nat_trans_id F). - exact (λ _ _ F, nat_trans_id F). - exact (λ _ _ _ _ _ _ _, nat_trans_id _). - exact (λ _ _ _ _ _ _ _, nat_trans_id _). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.catiso. Require Import UniMath.CategoryTheory.CategoryEquality. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Univalence.