 The left adjoint of this functor is the existential quantifier formula_27 and the right adjoint is the universal quantifier formula_28.That is, formula_29 is a functor that, for each subset formula_30, gives the subset formula_31 given by
those formula_33 in the image of formula_34 under formula_35.Similarly, the universal quantifier formula_36 is a functor that, for each subset formula_30, gives the subset formula_38 given by
those formula_33 whose preimage under formula_35 is contained in formula_34.