Definition Catlike_right_unitor (a b : category) : nat_trans (functor_composite (bindelta_pair_functor (functor_identity (functor_category a b)) (functor_composite (functor_to_unit (functor_category a b)) (constant_functor unit_category (functor_category b b) (functor_identity b)))) (functorial_composition a b b)) (functor_identity (functor_category a b)). Proof. use tpair. - intros x. exists (λ x, identity _). intros oba oba' f. exact (id_right _ @ !(id_left _)). - intros F F' f. apply (nat_trans_eq_alt). intros oba. simpl. unfold horcomp_data; simpl. rewrite (id_right _). rewrite (id_left _). apply id_right. 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.