Definition left_adjoint_to_repr_counit : post_comp w r ∙ post_comp w l ⟹ functor_identity _. Proof. use make_nat_trans. - exact (λ f, rassociator _ _ _ • (f ◃ ε) • runitor _). - abstract (intros f₁ f₂ τ ; cbn ; rewrite !vassocr ; rewrite rwhisker_rwhisker_alt ; rewrite !vassocl ; rewrite <- vcomp_runitor ; apply maponpaths ; rewrite !vassocr ; 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.