Filtered objects in extriangulated 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...

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

Tractarian objects and logical categories

It has been much debated whether the Tractarian objects are what Russell would have called particulars or whether they include also properties and relations. This paper claims that the debate is misguided: there is no logical category such that Wittgenstein intended the reader of the Tractatus to understand his objects either as providing examples of or as not providing examples of that categor...