fact: Definition binprod_ump_2 : UU := ∏ (a : B) (φ ψ : a --> p) (α : φ · binprod_cone_pr1 p ==> ψ · binprod_cone_pr1 p) (β : φ · binprod_cone_pr2 p ==> ψ · binprod_cone_pr2 p), ∃! (γ : φ ==> ψ), (γ ▹ binprod_cone_pr1 p = α) × (γ ▹ binprod_cone_pr2 p = β).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.PrecategoryBinProduct UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.Core.Univalence