The additivity of traces in stable $\infty$-categories

Abstract

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 $\mathrm{THH}(\mathbf{C})\to \mathrm{End}(1_{\mathbf{C}})$ 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.

12 pages, comments welcome ! New version: corrected typos, fixed some references, and added two remarks

References in corpus (1)

• Localization theorems in topological Hochschild homology and topological cyclic homology

Cited by in corpus (1)

• Characters and transfer maps via categorified traces