Definition functor_enrichment_data {V : monoidal_cat} {C₁ C₂ : category} (F : C₁ ⟶ C₂) (E₁ : enrichment C₁ V) (E₂ : enrichment C₂ V) : UU := ∏ (x y : C₁), E₁ ⦃ x , y ⦄ --> E₂ ⦃ F x , F y ⦄.
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.