Silting reduction and Calabi--Yau reduction of triangulated categories

Abstract

It is shown that the silting reduction $\ct/\thick\cp$ of a triangulated category $\ct$ with respect to a presilting subcategory $\cp$ can be realized as a certain subfactor category of $\ct$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\ct$ containing $\cp$ and the set of (pre)silting subcategories of $\ct/\thick\cp$. This is analogous to a result for Calabi-Yau reduction. This result is applied to show that Amiot-Guo-Keller's construction of $d$-Calabi-Yau triangulated categories with $d$-cluster-tilting objects takes silting reduction to Calabi-Yau reduction.

Section 5.5 in v4 removed: the formula (5.5.1) was a misunderstanding of the cited result in [KR1]. To appear in TAMS

References in corpus (8)

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• Calabi-Yau algebras
• On the representation dimension of artin algebras
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• Relative singularity categories III: Cluster resolutions
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• The realization of Verdier quotients as triangulated subfactors

Cited by in corpus (3)

• Internally Calabi-Yau algebras and cluster-tilting objects
• Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories
• Relative Singularity Categories