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Added a link, since I had to google to find the definition.
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David White
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On triangulated categories we have a notion of Bridgeland stability conditionsBridgeland stability conditions.

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

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 $hC$?

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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$\infty$-categorical understanding of Bridgeland stability conditions?

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Infinity $\infty$-categorical understanding of Bridgeland stability conditions?

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