Definition nat_trans_enrichment {V : monoidal_cat} {C₁ C₂ : category} {F G : C₁ ⟶ C₂} (τ : nat_trans_data F G) {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} (FE : functor_enrichment F E₁ E₂) (GE : functor_enrichment G E₁ E₂) : UU := ∏ (x y : C₁), mon_rinvunitor (E₁ ⦃ x , y ⦄) · GE x y #⊗ enriched_from_arr E₂ (τ x) · enriched_comp E₂ _ _ _ = mon_linvunitor (E₁ ⦃ x , y ⦄) · enriched_from_arr E₂ (τ y) #⊗ FE x y · enriched_comp E₂ _ _ _.
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.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.whiskering.