Semistable subcategories were introduced in the context of Mumford's GIT and interpreted
by King in terms of representation theory of finite dimensional algebras. Ingalls and Thomas …

It is proved that any tilting adjunction is completely described by an exact category with a
coherence property and the closure condition that exact sequences are acyclic. The …

In this paper, we consider a kind of ideal quotient of an extriangulated category such that the
ideal is the kernel of a functor from this extriangulated category to an abelian category. We …

We generalize the relative (co) tilting theory of Auslander-Solberg [9, 10] in the category mod
Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod …

Our first aim is to provide an analog of the Gabriel-Quillen embedding theorem for n-exact
categories. Also we give an example of an n-exact category that in not an n-cluster tilting …

In an ongoing project to classify all hereditary abelian categories, we provide a classification
of $\operatorname {Ext} $-finite directed hereditary abelian categories satisfying Serre …

One-sided exact categories appear naturally as instances of Grothendieck pretopologies. In
an additive setting they are given by considering the one-sided part of Keller's axioms …

Building on work of Jasso, we prove that any projectively generated $ d $-abelian category
is equivalent to a $ d $-cluster tilting subcategory of an abelian category with enough …

Let B be an extriangulated category with enough projectives and enough injectives. Let C be
a fully rigid subcategory of B which admits a twin cotorsion pair ((C, K),(K, D)). The quotient …

Pretorsion theories were defined in [11, 12] as “non-pointed torsion theories”, where the zero
object and the zero morphisms are replaced by a class of “trivial objects” and an ideal of …