0NJ4 Theorem 1.10. (see theorems 4.22 and 4.23) The accessible localization of (Cat𝒮)∞(\Cat_{\mathcal{S}})_{\infty} along the triangulated equivalences is equivalent to Cat∞ex\Cat_{\infty}^{\ex}, and the (further) localization of (Cat𝒮)∞(\Cat_{\mathcal{S}})_{\infty} along the Morita equivalences is equivalent to Cat∞perf\Cat_{\infty}^{\perf}.