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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
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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 $T$?
Edi …