Definition fully_faithful_enriched_functor_to_full {C₁ C₂ : category} {F : C₁ ⟶ C₂} {V : monoidal_cat} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} (EF : functor_enrichment F E₁ E₂) (HEF : fully_faithful_enriched_functor EF) : full F.
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.