Complements of partial silting objects in triangulated categories. (Chinese. English summary) Zbl 1438.18006
Summary: The existence of the complements of the presilting object \(P\) in a Krull-Schmidt triangulated category with a silting object \(T\) is investigated. It is shown that if all the indecomposable direct summands of \(P\) are generalized two-term related to \(T\), then there exist complements of \(P\). Consequently, \(P\) is partial silting. As an application, the presilting complexes over algebras which are derived equivalent to hereditary algebras are partial silting complexes.
MSC:
18C40 | Structured objects in a category (group objects, etc.) |
18G80 | Derived categories, triangulated categories |