  The bicategory of parameterized spectra has a remarkably rich structure. In
particular, it is possible to take traces in this bicategory, which give
classical invariants that count fixed points. We can also take equivariant
traces, which give significant generalizations of the classical invariants that
count periodic points.
  Unfortunately, the existence of these traces in general depends on technical
statements about the bicategory that can be difficult to verify directly. In
this paper, we demonstrate the effectiveness of two tools -- rigidity and
deformable functors -- by using them establish the structure we need to take
these equivariant traces and to construct periodic-point invariants in a formal
way.
