fact: Definition MonicToKernel' {x y : A} (M : Monic A x y) (CK : Cokernels.Cokernel (to_Zero A) M) : Kernels.Kernel (to_Zero A) (CokernelArrow CK) := @Kernel_up_to_iso2 A (to_Zero A) _ _ _ (CokernelArrow (Cokernel M)) (CokernelArrow CK) (iso_from_Cokernel_to_Cokernel (to_Zero A) (Cokernel M) CK) (CokernelCommutes _ _ _ _ _) (MonicToKernel M).
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive