Silting mutation in triangulated categories

Understand

In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e.

• `cluster tilting mutation' and `exceptional mutation'.
• In this paper we focus on `tilting mutation', which has a disadvantage that it is often impossible, i.e.
• some of summands of a tilting object can not be replaced to get a new tilting object.