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