Definition fundamental_bigroupoid : bicat. Proof. use build_bicategory. - exact two_type_bicat_data. - exact two_type_bicat_laws. - intros x y p₁ p₂ ; cbn in *. exact (HX x y p₁ p₂). 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.