Definition eso_ff_factorization_bicat_of_univ_cats : eso_ff_factorization bicat_of_univ_cats. Proof. intros C₁ C₂ F. refine (univalent_image F ,, functor_full_img _ ,, sub_precategory_inclusion _ _ ,, _). simple refine (_ ,, _ ,, _). - use essentially_surjective_is_eso. apply functor_full_img_essentially_surjective. - use cat_fully_faithful_is_fully_faithful_1cell. apply fully_faithful_sub_precategory_inclusion. - use nat_z_iso_to_invertible_2cell. exact (full_image_inclusion_commute_nat_iso F). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Eso. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInBicatOfUnivCats. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Require Import UniMath.Bicategories.Limits.Examples.BicatOfUnivCatsLimits.