  We show that in any symmetric monoidal category, if a weight for colimits is
absolute, then the resulting colimit of any diagram of dualizable objects is
again dualizable. Moreover, in this case, if an endomorphism of the colimit is
induced by an endomorphism of the diagram, then its trace can be calculated as
a linear combination of traces on the objects in the diagram. The formal nature
of this result makes it easy to generalize to traces in homotopical contexts
(using derivators) and traces in bicategories. These generalizations include
the familiar additivity of the Euler characteristic and Lefschetz number along
cofiber sequences, as well as an analogous result for the Reidemeister trace,
but also the orbit-counting theorem for sets with a group action, and a general
formula for homotopy colimits over EI-categories.
