fact: Definition disp_isBinCoproduct {x y : C} {xx : D x} {yy : D y} (p : BinCoproduct x y) (pp : D p) (ιι₁ : xx -->[ BinCoproductIn1 p ] pp) (ιι₂ : yy -->[ BinCoproductIn2 p ] pp) : UU := ∏ (w : C) (ww : D w) (f : x --> w) (ff : xx -->[ f ] ww) (g : y --> w) (gg : yy -->[ g ] ww), ∃! (hh : pp -->[ BinCoproductArrow p f g ] ww), (transportf (λ z, _ -->[ z ] _) (BinCoproductIn1Commutes _ _ _ p _ f g) (ιι₁ ;; hh) = ff) × (transportf (λ z, _ -->[ z ] _) (BinCoproductIn2Commutes _ _ _ p _ f g) (ιι₂ ;; hh) = gg).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total