Definition comp_essentially_surj_mor_inv2cell {h₁ : slice_bicat b₁} {h₂ : slice_bicat b₂} (α : h₁ --> pb_psfunctor B f h₂) : invertible_2cell (pr2 h₁ · f) (comp_essentially_surj_mor α · pr2 h₂) := comp_of_invertible_2cell (rwhisker_of_invertible_2cell _ (pr2 α)) (comp_of_invertible_2cell (rassociator_invertible_2cell _ _ _) (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ (pb_cell _ _)) (lassociator_invertible_2cell _ _ _))).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Bicategories.Core.Bicat. Import Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.UniversalArrow. Require Import UniMath.Bicategories.PseudoFunctors.Examples.PullbackFunctor. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Import PullbackFunctions.Notations.