Definition cell_are_companions {B : verity_double_bicat} (H : vertically_saturated B) {x y : B} {h₁ h₂ : x --> y} (τ : h₂ ==> h₁) {v₁ v₂ : x -|-> y} (c₁ : are_companions h₁ v₁) (c₂ : are_companions h₂ v₂) : v₁ ==> v₂ := let φ₁ := unit_are_companions c₁ in let ψ₂ := τ ▿s counit_are_companions c₂ in square_to_vertical_cell H (linvunitor _ ◃s (runitor _ ▹s ψ₂ ⋆v φ₁)).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. 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.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairs.