Assume that D is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor and a
cluster-tilting object T. We introduce the notion of ghost-tilting objects, and T [1]-tilting objects …

Assume that $\D $ is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor
and a cluster-tilting object $ T $. We introduce the notion of relative cluster tilting objects, and …

Assume that $\mathcal {D} $ is a Krull-Schmidt, Hom-finite triangulated category with a Serre
functor and a cluster-tilting object $ T $. We introduce the notion of relative cluster tilting …

Let $\mathcal C $ be a Krull-Schmidt triangulated category with shift functor $[1] $ and
$\mathcal R $ be a rigid subcategory of $\mathcal C $. We are concerned with the mutation …

Let T be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism
algebra Γ. Consider the functor T (T,−): T→ mod Γ. It induces a bijection from the …

For a triangulated category C with a cluster tilting subcategory T which contains infinitely
many indecomposable objects, the notion of weak T [1]-cluster tilting subcategories of C is …

Let (C, E, s) be an extriangulated category. We show that certain quotient categories of
extriangulated categories are equivalent to module categories by some restriction of functor …

We study two kinds of reduction processes of triangulated categories, that is, silting
reduction and Calabi–Yau reduction. It is shown that the silting reduction $\mathcal …

Let 𝒟 be a Krull–Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-
tilting object T. We introduce the notion of an F Λ-stable support τ-tilting module, induced by …

We prove that certain subquotient categories of extriangulated categories are abelian. As a
particular case, if an extriangulated category CC has a cluster-tilting subcategory XX, then …