This paper surveys some recent results, concerning the intrinsicness of natural subcategories of weakly approximable triangulated subcategories. We also review the results about uniqueness of enhancements of triangulated categories, with the aim of showing the fruitful interplay. In particular, we show how this leads to a vast generalization of a result by Rickard about derived invariance for schemes and rings.
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Canonaco et al. (2024) studied this question.
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