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