Definition univalent_image {C₁ C₂ : univalent_category} (F : C₁ ⟶ C₂) : univalent_category. Proof. use make_univalent_category. - exact (full_img_sub_precategory F). - use is_univalent_full_sub_category. exact (pr2 C₂). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.