∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {L : CategoryTheory.Functor C D} {F : CategoryTheory.Functor D C} {G : CategoryTheory.Functor C D}
  {R : CategoryTheory.Functor D C} (q : CategoryTheory.Adjunction.Quadruple L F G R) [inst_2 : F.Full]
  [inst_3 : F.Faithful] [CategoryTheory.Limits.HasPullbacks C] [CategoryTheory.Limits.HasPushouts D],
  CategoryTheory.Epi q.leftTriple.rightToLeft ↔ CategoryTheory.Mono q.rightTriple.leftToRight