Lemma dispadjunction_hom_weq' (c : C) (c' : C') (f : C'⟦F c, c'⟧) (d : D c) (d' : D' c') : (FF _ d -->[f] d') ≃ (d -->[η _ · # G f] GG _ d'). Proof. exists (homset_conj' _ _ _). apply (isweq_iso _ (homset_conj'_inv _ _ _)). - apply homset_conj'_inv_after_conj'. - apply homset_conj'_after_conj'_inv. 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.