 For example, the universal closure of
is

In category theory and the theory of elementary topoi, the universal quantifier can be understood as the right adjoint of a functor between power sets, the inverse image functor of a function between sets; likewise, the existential quantifier is the left adjoint.For a set formula_21, let formula_22 denote its powerset.For any function formula_23 between sets formula_21 and formula_25, there is an inverse image functor formula_26 between powersets, that takes subsets of the codomain of "f" back to subsets of its domain.