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On triangulated categories we have a notion of Bridgeland stability conditions.

Is there any known notion of "derived stability conditions" on a stable $\infty$-category $C$ such that they become Bridgeland stability conditions after passing to the homotopy category $hC$?

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  • $\begingroup$ I do not know much about the topic but try to have look at: arxiv.org/pdf/1501.04658.pdf $\endgroup$
    – Simone Virili
    Commented Mar 26, 2019 at 11:24
  • $\begingroup$ This looks useful @SimoneVirili! $\endgroup$
    – dumb
    Commented Mar 26, 2019 at 11:32

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Yes, this is chapter 7 of Fosco Loregian's thesis, linked from his webpage. The paper Simone Virili linked to is one of 3 papers making up the thesis. Specifically, Section 7.2.1 discusses the topology, after Bridgeland, and proves the comparison you asked for. The setting is a slight generalization of that of Bridgeland's original papers, as Loregian makes clear.

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  • $\begingroup$ Exactly what I was looking for, thanks! $\endgroup$
    – dumb
    Commented Mar 26, 2019 at 19:30

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