Definition pb_2cell_on_lunitor {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 (linvunitor_invertible_2cell g₁) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell (id₁ a₁) α) (lassociator_invertible_2cell (id₁ a₁) h g₂)) • (lunitor h ▹ g₂) = α) : lunitor (f /≃₁ α) = (pb_1cell_on_id f g₁ ▹ f /≃₁ α) • pb_1cell_on_comp f (linvunitor_invertible_2cell g₁) α • 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.