Definition path_right_adjoint_over_id_data {C : category} {D₁ D₂ : disp_cat C} (HD₁ : is_univalent_disp D₁) (HD₂ : is_univalent_disp D₂) {F : disp_functor (functor_identity C) D₁ D₂} {HF₁ HF₂ : right_adjoint_over_id_data F} (p₁ : disp_nat_z_iso (pr1 HF₁) (pr1 HF₂) (nat_z_iso_id (functor_identity C))) (p₂ : ∏ (x : C) (xx : D₁ x), (pr12 HF₁) x xx ;; p₁ x (F x xx) = transportf (λ z, _ -->[ z ] _) (!(id_right _)) ((pr12 HF₂) x xx)) (p₃ : ∏ (x : C) (xx : D₂ x), pr22 HF₁ x xx = transportf (λ z, _ -->[ z ] _) (id_left _) (♯F (p₁ x xx) ;; pr22 HF₂ x xx)) : HF₁ = HF₂.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq.