Definition cat_prebicat_nouniv_data : prebicat_data. Proof. use build_prebicat_data. - exact 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.