Non-semistable Exceptional Objects in Hereditary Categories

Gorenstein projective objects in Abelian categories

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...

gorenstein projective objects in abelian categories

let $mathcal {a}$ be an abelian category with enough projective objects and $mathcal {x}$ be a full subcategory of $mathcal {a}$. we define gorenstein projective objects with respect to $mathcal {x}$ and $mathcal{y}_{mathcal{x}}$, respectively, where $mathcal{y}_{mathcal{x}}$=${ yin ch(mathcal {a})| y$ is acyclic and $z_{n}yinmathcal{x}}$. we point out that under certain hypotheses, these two g...

Moduli of Bridgeland semistable objects on P

Let X be a smooth projective surface, Coh(X) the abelian category of coherent sheaves on X, and D(X) the bounded derived category of coherent sheaves on X. We study the Bridgeland stability conditions on D(X) and see that for some stability conditions on D(X) the moduli spaces of (semi)stable objects in D(X) coincide with the moduli spaces of (semi)stable coherent sheaves, while for some other ...

Objects in Triangulated Categories

We introduce the Calabi-Yau (CY) objects in a Hom-finite Krull-Schmidt triangulated k-category, and notice that the structure of the minimal, consequently all the CY objects, can be described. The relation between indecomposable CY objects and Auslander-Reiten triangles is provided. Finally we classify all the CY modules of selfinjective Nakayama algebras, determining this way the self-injectiv...

Injective objects in triangulated categories