  We prove two general factorization theorems for fixed-point invariants of
fibrations: one for the Lefschetz number and one for the Reidemeister trace.
These theorems imply the familiar multiplicativity results for the Lefschetz
and Nielsen numbers of a fibration. Moreover, the proofs of these theorems are
essentially formal, taking place in the abstract context of bicategorical
traces. This makes generalizations to other contexts straightforward.
