Definition left_adjoint_to_repr_unit : functor_identity _ ⟹ post_comp w l ∙ post_comp w r. Proof. use make_nat_trans. - exact (λ f, rinvunitor _ • (f ◃ η) • lassociator _ _ _). - abstract (intros f₁ f₂ τ ; cbn ; rewrite !vassocl ; rewrite rwhisker_rwhisker ; rewrite !vassocr ; rewrite rinvunitor_natural ; rewrite <- rwhisker_hcomp ; apply maponpaths_2 ; rewrite !vassocl ; rewrite vcomp_whisker ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions.