Definition fundamental_bigroupoid_is_univalent_2_1 : is_univalent_2_1 fundamental_bigroupoid. Proof. intros x y p₁ p₂. use isweq_iso ; cbn in *. - intros q. apply q. - intros q. induction q ; cbn. apply idpath. - intros q. induction q as [q Hq]. induction q ; cbn. use subtypePath ; cbn. + intro. apply (isaprop_is_invertible_2cell (C:=fundamental_bigroupoid)). + apply idpath. 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.