Definition product_enrichment_to_arr {x₁ y₁ : C₁} {x₂ y₂ : C₂} (fg : I_{V} --> product_enrichment_hom x₁ y₁ x₂ y₂) : (x₁ --> y₁) × (x₂ --> y₂) := enriched_to_arr E₁ (fg · semi_cart_tensor_pr1 HV _ _) ,, enriched_to_arr E₂ (fg · semi_cart_tensor_pr2 HV _ _).
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.opp_precat. Require Import UniMath.CategoryTheory.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Import MonoidalNotations.