  The postulates of comprehension and extensionality in set theory are based on
an inversion principle connecting set-theoretic abstraction and the property of
having a member. An exactly analogous inversion principle connects functional
abstraction and application to an argument in the postulates of the lambda
calculus. Such an inversion principle arises also in two adjoint situations
involving a cartesian closed category and its polynomial extension. Composing
these two adjunctions, which stem from the deduction theorem of logic, produces
the adjunction connecting product and exponentiation, i.e. conjunction and
implication.
