Definition factor_eso_ff_equiv : left_equivalence m. Proof. simple refine ((_ ,, (_ ,, _)) ,, (_ ,, _)). - exact inv. - use (fully_faithful_1cell_inv_map Hm). exact (lunitor _ • rinvunitor _ • (m ◃ ε^-1) • lassociator _ _ _). - exact ε. - apply (fully_faithful_to_conservative Hm). use (eq_is_invertible_2cell (!(fully_faithful_1cell_inv_map_eq Hm _))). cbn -[ε]. is_iso. - apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.Eso. Require Import UniMath.Bicategories.Limits.Pullbacks.