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 …

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 …

For a triangulated category TT, if CC is a cluster-tilting subcategory of TT, then the factor
category T/CT/C is an abelian category. Under certain conditions, the converse also holds …

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 be a triangulated category with shift functor [1] and R a rigid subcategory of C. We
introduce the notions of two-term R [1]-rigid subcategories, two-term (weak) R [1]-cluster …

Let be an extriangulated category with enough projectives P \mathcalP and enough
injectives I \mathcalI, and let be a contravariantly finite rigid subcategory of which contains P …

Let D be a triangulated category with a cluster tilting subcategory U. The quotient category
D/U is abelian; suppose that it has finite global dimension. We show that projection from D to …

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 …

In this paper, we study a close relationship between relative cluster tilting theory in
extriangulated categories and τ-tilting theory in module categories. Our main results show …