The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

We rst introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category.
This uni es the notion of an almost split sequence in an abelian category and that of an …

Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents.
Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the …

In this paper, we introduce the class of Cohen-Macaulay (= CM) dg (= differential graded)
modules over Gorenstein dg algebras and study their basic properties. We show that the …

Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any
cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable …

arXiv:0810.5546v2 [math.RT] 8 Nov 2008 Page 1 arXiv:0810.5546v2 [math.RT] 8 Nov 2008 THE
HALL ALGEBRA OF A SPHERICAL OBJECT BERNHARD KELLER, DONG YANG, AND …

In this article, we give a definition and a classification of 'higher'simple-minded systems in
triangulated categories generated by spherical objects with negative Calabi–Yau …

When the base connected cochain DG algebra is cohomologically bounded, it is proved that
the difference between the amplitude of a compact DG module and that of the DG algebra is …

Let k be an algebraically closed field and let T be the k-linear algebraic triangulated
category generated by aw-spherical object for an integer w. For certain values of w this …