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arXiv · 2109.01512

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

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

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Maxime Ramzi. 2022-08-18. The additivity of traces in stable $\infty$-categories. https://arxiv.org/abs/2109.01512

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