Definition fullsub_enrichment_data : enrichment_data (subcategory C (full_sub_precategory P)) V. Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _). - exact (λ x y, E ⦃ pr1 x , pr1 y ⦄). - exact (λ x, enriched_id E (pr1 x)). - exact (λ x y z, enriched_comp E (pr1 x) (pr1 y) (pr1 z)). - exact (λ x y f, enriched_from_arr E (pr1 f)). - exact (λ x y f, enriched_to_arr E f ,, tt). 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.Monoidal.Categories.