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Keywords:
triangulated category; colocalizing subcategory; Balmer-Favi cosupport; filtration
triangulated category; colocalizing subcategory; Balmer-Favi cosupport; filtration
Summary:
Suppose $\mathcal {T}$ is a rigidly-compactly generated tensor triangulated category and $\mathcal {K}$ is a compactly generated triangulated category on which $\mathcal {T}$ acts, in the sense of Stevenson. We prove that if $\rm {Spc}(\mathcal {T}^{c})$ is Noetherian and $\mathcal {K}$ is stable, then each object in $\mathcal {K}$ has a unique functorial tower, filtered by Balmer-Favi cosupports. This is an analogy of Stevenson's work on filtrations by Balmer-Favi supports.
References:
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