Definition invertible_2cell_ps_base_weq {F G : ps_base} (η ε : F --> G) : (∏ (X : C), invertible_2cell (η X) (ε X)) ≃ invertible_2cell η ε. Proof. refine (make_weq (invertible_2cell_ps_base η ε) _). use isweq_iso. - exact (invertible_2cell_ps_base_inv η ε). - intros α. apply funextsec ; intro X. apply subtypePath. { intro ; apply isaprop_is_invertible_2cell. } reflexivity. - intros α. apply subtypePath. { intro ; apply isaprop_is_invertible_2cell. } apply funextsec ; intro X. 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.