Abstract
We study two kinds of reduction processes of triangulated categories, that is, silting reduction and CalabiâYau reduction. It is shown that the silting reduction $\mathcal {T}/\mathsf {thick}\mathcal {P}$ of a triangulated category $\mathcal {T}$ with respect to a presilting subcategory $\mathcal {P}$ can be realized as a certain subfactor category of $\mathcal {T}$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\mathcal {T}$ containing $\mathcal {P}$ and the set of (pre)silting subcategories of $\mathcal {T}/\mathsf {thick}\mathcal {P}$. This result is applied to show that the AmiotâGuoâKeller construction of $d$-CalabiâYau triangulated categories with $d$-cluster-tilting objects takes silting reduction to CalabiâYau reduction.
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