proposition: Lemma is_nat_trans_coproduct_nat_trans_data : is_nat_trans _ _ coproduct_nat_trans_data.
proof: Proof. intros a b k; simpl. eapply pathscomp0. apply (precompWithCoproductArrow I D (HD (λ i : I, (F i) a)) (HD (λ i : I, (F i) b))). apply pathsinv0. eapply pathscomp0; [apply postcompWithCoproductArrow|]. apply maponpaths, funextsec; intro i. now rewrite (nat_trans_ax (f i)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.whiskering