proposition: Lemma BinCoproductArrowUnique (a b : C) (CC : BinCoproduct a b) (x : C) (f : a --> x) (g : b --> x) (k : BinCoproductObject CC --> x) : BinCoproductIn1 CC · k = f → BinCoproductIn2 CC · k = g → k = BinCoproductArrow CC f g.
proof: Proof. intros H1 H2. set (H := tpair (λ h, dirprod _ _ ) k (make_dirprod H1 H2)). set (H' := (pr2 (isBinCoproduct_BinCoproduct CC _ f g)) H). apply (base_paths _ _ H'). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.ProductCategory