Lemma dispadjunction_hom_weq (c : C) (c' : C') (g : C⟦c, G c'⟧) (d : D c) (d' : D' c') : (d -->[g] GG _ d') ≃ (FF _ d -->[# F g · ε _] d'). Proof. exists (homset_conj_inv _ _ _). apply (isweq_iso _ (homset_conj _ _ _)). - apply homset_conj_after_conj_inv. - apply homset_conj_inv_after_conj. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. 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.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences.