Definition cat_with_enrichment_alt_data_help {V : monoidal_cat} (ob : UU) (arr : ob -> ob -> V) : UU := ∑ (mor : ob -> ob -> UU), (∏ (x : ob), mor x x) × (∏ (x y z : ob), mor x y → mor y z → mor x z) × (∏ (x y : ob), mor x y → I_{V} --> arr x y) × (∏ (x y : ob), I_{V} --> arr x y → mor x y).
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.