Complete weight structures on stable categories are determined by their weight hearts and can be used to reconstruct categories from hearts via two-step completions when paired with compatible weak t-structures.
[Bon10] Mikhail V Bondarko,Weight structures vs
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Unbounded Weight Structures: (Re)construction and Completion
Complete weight structures on stable categories are determined by their weight hearts and can be used to reconstruct categories from hearts via two-step completions when paired with compatible weak t-structures.