  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.
