Definition image_proj_enrichment : functor_enrichment (functor_full_img _) E₁ image_enrichment. Proof. simple refine (_ ,, _ ,, _ ,, _). - exact (λ x y, EF x y). - abstract (intro x ; cbn ; exact (functor_enrichment_id EF x)). - abstract (intros x y z ; cbn ; exact (functor_enrichment_comp EF x y z)). - abstract (intros x y f ; exact (functor_enrichment_from_arr EF 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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.FullSubEnriched. Require Import UniMath.CategoryTheory.Monoidal.Categories.