proposition: Lemma SumOfKernelCokernelPairs {M : PreAdditive} {x y z X Y Z : M} (xX : BinDirectSum x X) (yY : BinDirectSum y Y) (zZ : BinDirectSum z Z) {f : x --> y} {g : y --> z} {f' : X --> Y} {g' : Y --> Z} : isKernelCokernelPair f g -> isKernelCokernelPair f' g' -> isKernelCokernelPair (directSumMap xX yY f f') (directSumMap yY zZ g g').
proof: Proof. intros i i'. exists (SumOfKernels _ _ _ f g f' g' (pr1 i) (pr1 i')). exact (SumOfCokernels _ _ _ f g f' g' (pr2 i) (pr2 i')). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Notations UniMath.MoreFoundations.PartA 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.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.BinDirectSums UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Subcategory.Full UniMath.MoreFoundations.Propositions