∀ {X' X : Type u_1} {Y : Pointed} (f : X' ⟶ X) (g : X ⟶ (CategoryTheory.forget Pointed).obj Y),
  { toFun := fun f => f.toFun ∘ some, invFun := fun f => { toFun := fun o => Option.elim o Y.point f, map_point := ⋯ },
          left_inv := ⋯, right_inv := ⋯ }.symm
      (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (typeToPointed.map f)
      ({ toFun := fun f => f.toFun ∘ some,
            invFun := fun f => { toFun := fun o => Option.elim o Y.point f, map_point := ⋯ }, left_inv := ⋯,
            right_inv := ⋯ }.symm
        g)