Definition all_is_adjequiv_is_is_adjequiv {F G : ps_base} (η : F --> G) : (∏ (X : C), left_adjoint_equivalence (η X)) ≃ left_adjoint_equivalence η. Proof. refine (make_weq (all_is_adjequiv_to_is_adjequiv η) _). use isweq_iso. - exact (is_adjequiv_to_all_is_adjequiv η). - intros Hη. apply funextsec ; intro X. use subtypePath. { intro. do 2 apply isapropdirprod ; try (apply D) ; apply isaprop_is_invertible_2cell. } reflexivity. - intros Hη. use subtypePath. { intro. do 2 apply isapropdirprod ; try (apply ps_base) ; apply isaprop_is_invertible_2cell. } reflexivity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique.