Definition invertible_2cell_ps_base {F G : ps_base} (η ε : F --> G) : (∏ (X : C), invertible_2cell (η X) (ε X)) → invertible_2cell η ε. Proof. intros α. use tpair. - intros X. exact (α X). - apply all_is_invertible_is_is_invertible_2cell. apply α. 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.