0NMW Proof. The proof is a consequence of the equivalences FunL(Pre((Cat∞perf)ω)∗,𝒟)\displaystyle\mathrm{Fun}^{\mathrm{L}}(\mathrm{Pre}((\Cat_{\infty}^{\perf})^{\omega})_{*},{\mathcal{D}}) ≃Fun((Cat∞perf)ω,𝒟)\displaystyle\simeq\mathrm{Fun}((\Cat_{\infty}^{\perf})^{\omega},{\mathcal{D}}) ≃Funflt(Ind((Cat∞perf)ω),𝒟)\displaystyle\simeq\mathrm{Fun}_{\mathrm{flt}}(\Ind((\Cat_{\infty}^{\perf})^{\omega}),{\mathcal{D}}) ≃Funflt(Cat∞perf,𝒟),\displaystyle\simeq\mathrm{Fun}_{\mathrm{flt}}(\Cat_{\infty}^{\perf},{\mathcal{D}})\,, where the first follows from [52, 5.1.5.6] and the fact that 𝒟{\mathcal{D}} is pointed, and the last follows from corollary 4.25. ∎