∀ (X : Pointed) (Y : Bipointed) (f : pointedToBipointedFst.obj X ⟶ Y),
  (fun f => { toFun := fun o => Option.elim o Y.toProd.2 f.toFun, map_fst := ⋯, map_snd := ⋯ })
      ((fun f => { toFun := f.toFun ∘ some, map_point := ⋯ }) f) =
    f