Definition cat_with_enrichment_alt_data (V : monoidal_cat) : UU := ∑ (ob : UU) (arr : ob -> ob -> V), (∏ (x : ob), I_{V} --> arr x x) × (∏ (x y z : ob), arr y z ⊗ arr x y --> arr x z) × cat_with_enrichment_alt_data_help ob arr.
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.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.Enriched. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.UnderlyingCategory. Import MonoidalNotations.