∀ {C₁ : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C₁] [inst_1 : CategoryTheory.Abelian C₁]
  [inst_2 : HasDerivedCategory C₁] {C₂ : Type u₂} [inst_3 : CategoryTheory.Category.{v₂, u₂} C₂]
  [inst_4 : CategoryTheory.Abelian C₂] [inst_5 : HasDerivedCategory C₂] (F F_1 : CategoryTheory.Functor C₁ C₂)
  (e_F : F = F_1) [inst_6 : F.Additive] [inst_7 : CategoryTheory.Limits.PreservesFiniteLimits F]
  [inst_8 : CategoryTheory.Limits.PreservesFiniteColimits F], F.mapDerivedCategory = F_1.mapDerivedCategory