  We present a generalization of the multiplier ideal version of inversion of
adjunction, often known as the restriction theorem, to centers of arbitrary
codimension. We approach inversion of adjunction from the subadjunction point
of view. Let X be a smooth complex projective variety and let Z be an
exceptional log-canonical center of an effective Q-divisor D on some dense open
subset of X that contains the generic point of Z. Any subvariety of X can be
expressed as such a center for some D. We define an adjoint ideal that measures
how non-klt (X, D) is outside the generic point of Z. Our main theorem is that
this adjoint ideal restricts on Z to the multiplier ideal of an appropriate
boundary constructed in the same manner as the boundary in Kawamata's
subadjunction theorem. Our theorem extends Kawamata's subadjunction theorem and
implies that, in general, the boundary in Kawamata's subadjunction is klt if
and only if Z is an exceptional log-canonical center of (X, D).
