Definition enrichment_data_hom_weq {C : precategory_data} {V : monoidal_cat} (HV : is_univalent V) (E₁ E₂ : enrichment_data C V) : (pr1 E₁ = pr1 E₂) ≃ ∏ (x y : C), z_iso (pr1 E₁ x y) (pr1 E₂ x y) := (weqonsecfibers _ _ (λ x, weqonsecfibers _ _ (λ y, _ ,, HV _ _) ∘ weqtoforallpaths _ _ _) ∘ weqtoforallpaths _ _ _)%weq.
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.covyoneda. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import MonoidalNotations.