Definition strict_cat_prebicat_data : prebicat_data. Proof. use build_prebicat_data. - exact setcategory. - 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.Setcategories. 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.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Strictness. Require Import UniMath.Bicategories.Core.Univalence.