∀ {C : Type u_5} [inst : CategoryTheory.Category.{u_2, u_5} C] {D : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_2, u_3} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) {J : Type u_1} [inst_2 : CategoryTheory.Category.{u_4, u_1} J] {K : CategoryTheory.Functor J C} (Y : D),
  CategoryTheory.CategoryStruct.comp (adj.coconesIsoComponentHom Y) (adj.coconesIsoComponentInv Y) =
    CategoryTheory.CategoryStruct.id (((CategoryTheory.cocones J D).obj (Opposite.op (K.comp F))).obj Y)