∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Preadditive C] {D : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.Abelian D] (F : CategoryTheory.Functor C D)
  (G : CategoryTheory.Functor D C) [G.PreservesZeroMorphisms] [CategoryTheory.Limits.PreservesFiniteLimits G]
  (i : F.comp G ≅ CategoryTheory.Functor.id C), CategoryTheory.Limits.HasKernels C