proposition: Lemma AdditiveFunctorPreservesBinDirectSums {A B : CategoryWithAdditiveStructure} (F : AdditiveFunctor A B) : PreservesBinDirectSums F.
proof: Proof. intros a1 a2 DS. use make_isBinDirectSum. - use (AdditiveFunctorPreservesBinDirectSums_idin1 F DS). - use (AdditiveFunctorPreservesBinDirectSums_idin2 F DS). - use (AdditiveFunctorPreservesBinDirectSums_unit1 F DS). - use (AdditiveFunctorPreservesBinDirectSums_unit2 F DS). - use (AdditiveFunctorPreservesBinDirectSums_id F DS). 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