Definition universal_coprod_cocone_has_ump_1 : bincoprod_ump_1 p. Proof. intro q. use make_bincoprod_1cell. - exact (right_adjoint (Hp q) (bincoprod_cocone_inl q ,, bincoprod_cocone_inr q)). - apply z_iso_to_inv2cell. exact (pr1 (category_binproduct_z_iso_inv _ _ (nat_z_iso_pointwise_z_iso (counit_nat_z_iso_from_adj_equivalence_of_cats (Hp q)) (bincoprod_cocone_inl q ,, bincoprod_cocone_inr q)))). - apply z_iso_to_inv2cell. exact (pr2 (category_binproduct_z_iso_inv _ _ (nat_z_iso_pointwise_z_iso (counit_nat_z_iso_from_adj_equivalence_of_cats (Hp q)) (bincoprod_cocone_inl q ,, bincoprod_cocone_inr q)))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Section UniversalFromUMP. End UniversalFromUMP.