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 …

Let C be a set of objects in a triangulated compactly generated category T. We denote by
\calU_C\,(_C\calU) the smallest suspended subcategory closed under coproducts which …

In this article we further study the full subcategories of the category of finitely generated
modules over an Artin algebra introduced in Platzeck and Pratti, consisting of the modules …

We study suspended subcategories of the bounded derived category D b (mod H), where H
is a tame hereditary k-algebra. First, we consider U_M the smallest suspended subcategory …

Let A be an artin algebra and modA the category of finitely generated A-modules. Unless
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …

In this article, we introduce the notion of {\it concentric twin cotorsion pair} on a triangulated
category. This notion contains the notions of $ t $-structure, cluster tilting subcategory, co-$ t …

We consider filtrations of objects in an abelian category induced by a tilting object T of
homological dimension at most two. We define three extension closed subcategories and …

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 …

A finite directed category is ak-linear category with finitely many objects and an underlying
poset structure, where k is an algebraically closed field. This concept unifies structures such …

In the paper of Keller and Reiten, it was shown that the quotient of a triangulated category
(with some conditions) by a cluster tilting subcategory becomes an abelian category. After …