  We prove a version of J.P. May's theorem on the additivity of traces, in
symmetric monoidal stable $\infty$-categories. Our proof proceeds via a
categorification, namely we use the additivity of topological Hochschild
homology as an invariant of stable $\infty$-categories and construct a morphism
of spectra $\mathrm{THH}(\mathbf C)\to \mathrm{End}(\mathbf 1_\mathbf C)$ for
$\mathbf C$ a stably symmetric monoidal rigid $\infty$-category. We also
explain how to get a more general statement involving traces of finite
(homotopy) colimits.
