∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {D : Type u_2} [inst_3 : CategoryTheory.Category.{u_1, u_2} D]
  [inst_4 : CategoryTheory.MonoidalCategory D] [inst_5 : CategoryTheory.BraidedCategory D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (a : F ⊣ G) [inst_6 : F.Braided]
  [inst_7 : G.LaxBraided] [inst_8 : a.IsMonoidal] (Y : CategoryTheory.CommMon D),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.mapCommMonIdIso.inv
            (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.mapCommMonNatTrans a.unit)
              CategoryTheory.Functor.mapCommMonCompIso.hom)).app
        (G.mapCommMon.obj Y))
      (G.mapCommMon.map
        ((CategoryTheory.CategoryStruct.comp CategoryTheory.Functor.mapCommMonCompIso.inv
              (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.mapCommMonNatTrans a.counit)
                CategoryTheory.Functor.mapCommMonIdIso.hom)).app
          Y)) =
    CategoryTheory.CategoryStruct.id (G.mapCommMon.obj Y)