Definition one_type_2cell_iso : locally_groupoid one_types. Proof. intros X Y f g α. refine (invhomot α ,, _). split ; cbn. - apply funextsec. intro x. apply pathsinv0r. - apply funextsec. intro x. apply pathsinv0l. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique.