proposition: Lemma KernelInOp {x y z : A} (f1 f2 : A⟦x, y⟧) (g : A⟦y, z⟧) (K : Kernel Z g) (H1 : f1 · g = ZeroArrow Z _ _) (H2 : f2 · g = ZeroArrow Z _ _) : KernelIn Z K _ (to_binop _ _ f1 f2) (KernelInOp_Eq f1 f2 g H1 H2) = to_binop _ _ (KernelIn Z K _ f1 H1) (KernelIn Z K _ f2 H2).
proof: Proof. use KernelInsEq. rewrite KernelCommutes. rewrite (to_postmor_linear' (A:=A)). rewrite KernelCommutes. rewrite KernelCommutes. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels