proposition: Lemma isAdditiveCriteria {A B : CategoryWithAdditiveStructure} (F : functor A B) (H : PreservesBinDirectSums F) : isAdditiveFunctor F.
proof: Proof. use make_isAdditiveFunctor. intros a1 a2. split. - intros f g. cbn. apply (isAdditiveCriteria_BinOp F H f g). - set (tmp := isAdditiveCriteria_preservesUnel F H a1 a2). unfold to_unel in tmp. apply tmp. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.BinDirectSums