Definition representable_full {C : bicat} {X Y Z : C} {f : C⟦X,Y⟧} {g : C⟦Y,X⟧} (η : id₁ X ==> g ∘ f) (θ : f ∘ g ==> id₁ Y) (Hη : is_invertible_2cell η) (k₁ k₂ : C⟦Z,X⟧) (α : f ∘ k₁ ==> f ∘ k₂) : k₁ ==> k₂. Proof. refine (_ o rinvunitor _). refine (_ o η ▻ _). refine (_ o lassociator _ _ _). refine (_ o g ◅ α). refine (_ o rassociator _ _ _). refine (_ o Hη^-1 ▻ k₂). apply runitor. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.