ScalingStacks

Lemma 10.1. The functor

$$THH\colon\Cat_{\mathcal{S}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathcal{S}$$

induces a functor of $\infty$-categories

$$THH\colon\Cat_{\infty}^{\ex}\simeq\mathrm{N}((\Cat_{\mathcal{S}})^{\mathrm{c}})[W^{-1}]\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathrm{N}((\mathcal{S})^{\mathrm{c}})[W^{-1}]\simeq{\mathcal{S}}_{\infty}.$$