Definition pb_2cell_on_lassociator {a₁ a₂ a₃ a₄ b₁ b₂ : B} (f : b₁ --> b₂) {g₁ : a₁ --> b₂} {g₂ : a₂ --> b₂} {g₃ : a₃ --> b₂} {g₄ : a₄ --> b₂} {h₁ : a₁ --> a₂} {h₂ : a₂ --> a₃} {h₃ : a₃ --> a₄} (α : invertible_2cell g₁ (h₁ · g₂)) (β : invertible_2cell g₂ (h₂ · g₃)) (γ : invertible_2cell g₃ (h₃ · g₄)) (p : comp_of_invertible_2cell α (comp_of_invertible_2cell (lwhisker_of_invertible_2cell h₁ (comp_of_invertible_2cell β (comp_of_invertible_2cell (lwhisker_of_invertible_2cell h₂ γ) (lassociator_invertible_2cell h₂ h₃ g₄)))) (lassociator_invertible_2cell h₁ (h₂ · h₃) g₄)) • (lassociator h₁ h₂ h₃ ▹ g₄) = comp_of_invertible_2cell (comp_of_invertible_2cell α (comp_of_invertible_2cell (lwhisker_of_invertible_2cell h₁ β) (lassociator_invertible_2cell h₁ h₂ g₃))) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell (h₁ · h₂) γ) (lassociator_invertible_2cell (h₁ · h₂) h₃ g₄))) : (f /≃₁ α ◃ pb_1cell_on_comp f β γ) • pb_1cell_on_comp f α _ • f /≃₂ p = lassociator _ _ _ • (pb_1cell_on_comp f α β ▹ _) • pb_1cell_on_comp f _ γ.
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.