Definition make_is_binary_coprod_enriched_from_underlying (BPV : BinProducts V) (a : enriched_binary_coprod_cocone) (prod : isBinCoproduct C x y a (enriched_coprod_cocone_in1 a) (enriched_coprod_cocone_in2 a)) (HV : conservative_moncat V) : is_binary_coprod_enriched a. Proof. use (make_is_binary_coprod_enriched_from_z_iso BPV). intros w. use HV. use isweq_iso. - exact (coprod_from_underlying_arr_map BPV a prod w). - exact (coprod_from_underlying_arr_map_eq₁ BPV a prod w). - exact (coprod_from_underlying_arr_map_eq₂ BPV a prod w). 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.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Import MonoidalNotations. Section BinaryCoproductFromUnderlying. End BinaryCoproductFromUnderlying.