We prove that some subquotient categories of exact categories are abelian. This
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …

As a general framework for the studies of $ t $-structures on triangulated categories and
torsion pairs in abelian categories, we introduce the notions of extriangulated categories …

Based on Beligiannis's theory in [Beligiannis, A.(2000). Relative homological algebra and
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …

The notion of 𝒟-mutation pairs of subcategories in an abelian category is defined in this
article. When (𝒵, 𝒵) is a 𝒟-mutation pair in an abelian category 𝒜, the quotient category 𝒵∕ …

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 …

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and extension-closed subcategories of triangulated …

Happel [6] and Cline, Parshall and Scott [4] showed that the tilting functors of Happel and
Ringel [8] can be interpreted in terms of an equivalence of derived categories of the module …

Let be a-angulated category with d-suspension functor. Our main results show that every
Serre functor on is a-angulated functor. We also show that has a Serre functor if and only if …

In the preceding part (I) of this paper, we showed that for any torsion pair (ie, t-structure
without the shift-closedness) in a triangulated category, there is an associated abelian …

We generalize tilting with respect to a tilting module of projective dimension at most one for
an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our …