∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasKernels C] (f : CategoryTheory.Arrow C),
  (CategoryTheory.Limits.ker C).obj f = CategoryTheory.Limits.kernel f.hom