∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : CategoryTheory.Adjunction.CoreHomEquiv F G)
  (Y : D),
  (CategoryTheory.Adjunction.mkOfHomEquiv adj).counit.app Y =
    (adj.homEquiv (G.obj Y) Y).symm (CategoryTheory.CategoryStruct.id (G.obj Y))