Definition adjequiv_ps_base_weq (F G : ps_base) : (∏ (X : C), adjoint_equivalence (F X) (G X)) ≃ adjoint_equivalence F G. Proof. refine (make_weq (adjequiv_ps_base F G) _). use isweq_iso. - exact (adjequiv_ps_base_inv F G). - intros η. apply funextsec ; intro X. use total2_paths_b. + reflexivity. + cbn. use subtypePath. { intro. do 2 apply isapropdirprod ; try (apply D) ; apply isaprop_is_invertible_2cell. } reflexivity. - intros η. use total2_paths_b. + reflexivity. + cbn. 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.