ScalingStacks

0NME

Lemma 5.23. The full subcategory (Cat∞perf)ω⊂Cat∞perf(\Cat_{\infty}^{\perf})^{\omega}\subset\Cat_{\infty}^{\perf} of compact small stable idempotent-complete ∞\infty-categories is essentially small.

0NMF

Proof. The result follows from the fact that Cat∞perf\Cat_{\infty}^{\perf} is an accessible localization of Cat∞ex\Cat_{\infty}^{\ex}, and Cat∞ex\Cat_{\infty}^{\ex} itself is an accessible localization of the finitely presentable ∞\infty-category of small spectral categories via theorem 1.10. ∎

Original mathematics by the credited authors. Source collection and HTML conversion remain in progress.

Andrew J. Blumberg, David Gepner, Goncalo Tabuada

Original source: arXiv:1001.2282v4