  We prove two general decomposition theorems for fixed-point invariants: one
for the Lefschetz number and one for the Reidemeister trace. These theorems
imply the familiar additivity results for these invariants. Moreover, the
proofs of these theorems are essentially formal, taking place in the abstract
context of bicategorical traces. This makes it straightforward to generalize
the theory to analogous invariants in other contexts, such as equivariant and
fiberwise homotopy theory.
