Definition functor_id_enrichment_fully_faithful {V : monoidal_cat} {C : category} (E : enrichment C V) : fully_faithful_enriched_functor (functor_id_enrichment E). Proof. intros x y. apply is_z_isomorphism_identity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.Limits.Terminal. Import MonoidalNotations.