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LocalizeAndConquer
LocalizeAndConquer
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Let T be a compactly generated triangulated category and let T' be a localizing subcategory. Is it automatic that T' is comapctly generated by $T^c \cap T'$, where $T^c$ is compact objects of $T$?

Edit: I would be interested if there is a useful sufficient criteria (that takes advantage of the compact generation of T)?

Let T be a compactly generated triangulated category and let T' be a localizing subcategory. Is it automatic that T' is comapctly generated by $T^c \cap T'$, where $T^c$ is compact objects of $T$?

Let T be a compactly generated triangulated category and let T' be a localizing subcategory. Is it automatic that T' is comapctly generated by $T^c \cap T'$, where $T^c$ is compact objects of $T$?

Edit: I would be interested if there is a useful sufficient criteria (that takes advantage of the compact generation of T)?

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LocalizeAndConquer
LocalizeAndConquer
  • 23
  • 3

Subcategory of compactly generated triangulated category

Let T be a compactly generated triangulated category and let T' be a localizing subcategory. Is it automatic that T' is comapctly generated by $T^c \cap T'$, where $T^c$ is compact objects of $T$?