  We define a duality operation connecting closure operations, interior
operations, and test ideals, and describe how the duality acts on common
constructions such as trace, torsion, tight and integral closures, and
divisible submodules. This generalizes the relationship between tight closure
and tight interior given in [Epstein-Schwede 2014] and allows us to extend
commonly used results on tight closure test ideals to operations such as those
above.
