Definition fundamental_bigroupoid_1cell_equivalence {x y : fundamental_bigroupoid} (p : fundamental_bigroupoid⟦x,y⟧) : left_equivalence p. Proof. use tpair. - refine (!p ,, _). split ; cbn. + exact (! (pathsinv0r p)). + exact (pathsinv0l p). - split ; cbn. + apply fundamental_groupoid_2cell_iso. + apply fundamental_groupoid_2cell_iso. 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.