Definition homset_conj {c : C} {c' : C'} (g : C⟦c, G c'⟧) (d : D c) (d' : D' c') : (FF _ d -->[#F g · ε _] d') -> (d -->[g] GG _ d'). Proof. set (equiv := φ_adj_after_φ_adj_inv A g : η c · # G (# F g · ε c') = g). exact (λ beta, transportf _ equiv (homset_conj' _ _ _ beta)). 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.