Definition orthogonal_left_right_to_equiv : left_equivalence f. Proof. simple refine ((_ ,, (_ ,, _)) ,, _ ,, _) ; cbn. - refine (orthogonal_lift_1 _ _ _ α). exact (orthogonal_lifting fact_B f f Lf Rf). - exact (inv_of_invertible_2cell (orthogonal_lift_1_comm_left _ _ _ α)). - exact ((orthogonal_lift_1_comm_right _ _ _ α)). - apply property_from_invertible_2cell. - apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.OrthogonalFactorization.Orthogonality.