Definition to_eso_slice (Hα : is_eso (pr1 α)) : is_eso α. Proof. use make_is_eso. - use is_univalent_2_1_slice_bicat. exact HB. - exact (to_eso_full_slice Hα). - exact (to_eso_faithful_slice Hα). - exact (to_eso_essentially_surjective_slice Hα). 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.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.Eso. Section FromMorphismInSlice. Section FromFullyFaithfulSlice. End FromFullyFaithfulSlice. End FromMorphismInSlice.