Definition adjequiv_ps_base_inv (F G : ps_base) : adjoint_equivalence F G → (∏ (X : C), adjoint_equivalence (F X) (G X)). Proof. intros η X. use tpair. - exact (pr1 η X). - apply is_adjequiv_to_all_is_adjequiv. apply η. 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.