Definition coprod_enriched_to_prod (PV : Products J V) (a : enriched_coprod_cocone) (w : C) : E ⦃ a , w ⦄ --> PV (λ j, E ⦃ D j , w ⦄). Proof. use ProductArrow. exact (λ j, precomp_arr E w (enriched_coprod_cocone_in a j)). Defined.
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.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Coproducts. Import MonoidalNotations. Section CoproductFromUnderlying. End CoproductFromUnderlying.