Definition pb_ump_mor_left_adjoint_equivalence {B : bicat} {b₁ b₂ b₃ : B} {f : b₁ --> b₃} {g : b₂ --> b₃} (cone₁ cone₂ : pb_cone f g) (H₁ : has_pb_ump cone₁) (H₂ : has_pb_ump cone₂) : left_adjoint_equivalence (pb_ump_mor H₁ cone₂). Proof. use equiv_to_adjequiv. simple refine ((_ ,, (_ ,, _)) ,, (_ ,, _)). - exact (pb_ump_mor H₂ cone₁). - exact (pb_ump_mor_left_adjoint_equivalence_unit cone₁ cone₂ H₁ H₂). - exact ((pb_ump_mor_left_adjoint_equivalence_unit_inv2cell cone₂ cone₁ H₂ H₁)^-1). - apply pb_ump_mor_left_adjoint_equivalence_unit_inv2cell. - apply is_invertible_2cell_inv. Defined.
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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderInvertibles. Require Import UniMath.Bicategories.Limits.Pullbacks.