Definition pb_2cell_on_runitor {a₁ a₂ b₁ b₂ : B} (f : b₁ --> b₂) {g₁ : a₁ --> b₂} {g₂ : a₂ --> b₂} {h : a₁ --> a₂} (α : invertible_2cell g₁ (h · g₂)) (p : comp_of_invertible_2cell α (comp_of_invertible_2cell (lwhisker_of_invertible_2cell h (linvunitor_invertible_2cell g₂)) (lassociator_invertible_2cell h (id₁ a₂) g₂)) • (runitor h ▹ g₂) = α) : runitor (f /≃₁ α) = (f /≃₁ α ◃ pb_1cell_on_id f g₂) • pb_1cell_on_comp f α (linvunitor_invertible_2cell g₂) • f /≃₂ p.
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.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Limits.Pullbacks.