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View article: Quotient categories with exact structure from $(n+2)$-rigid subcategories in extriangulated categories
Quotient categories with exact structure from $(n+2)$-rigid subcategories in extriangulated categories Open
In this work we introduce the notion of higher $\mathbb{E}$-extension groups for an extriangulated category $\mathcal{C}$ and study the quotients $\mathcal{X}_{n+1}^{\vee}/[\mathcal{X}]$ and $\mathcal{X}_{n+1}^{\wedge}/[\mathcal{X}]$ when …
View article: Cut notions in extriangulated categories related to Auslander-Buchweitz theory and cotorsion theory
Cut notions in extriangulated categories related to Auslander-Buchweitz theory and cotorsion theory Open
In this work we introduce notions in Auslander-Buchweitz theory and cotorsion theory in extriangulated categories which extend the given ones for abelian categories. Although these notions have been already developed for extriangulated cat…
View article: Stratifying systems and g-vectors
Stratifying systems and g-vectors Open
View article: Stratifying systems and $g$-vectors
Stratifying systems and $g$-vectors Open
In this paper we study the Cartan matrix associated to the Ext-projective stratifying system induced by a basic and $τ$-rigid object $M$ in mod$(A)$ by means of the $g$-vectors of the indecomposable direct summands of $M$. In particular we…
View article: Standardly stratified lower triangular $\mathbb{K}$-algebras with enough idempotents
Standardly stratified lower triangular $\mathbb{K}$-algebras with enough idempotents Open
In this paper we study the lower triangular matrix $\mathbb{K}$-algebra $Λ:=\left[\begin{smallmatrix} T & 0 \\ M & U \end{smallmatrix}\right],$ where $U$ and $T$ are basic $\mathbb{K}$-algebras with enough idempotents and $M$ is an $U$-$T$…
View article: Cokernels of the Cartan matrix and stratifying systems
Cokernels of the Cartan matrix and stratifying systems Open
We study the cokernel of the application given by the Cartan Matrix $C_Λ$ of a finite dimensional $k$-algebra $Λ.$ This produces a finitely generated abelian group, the Cartan group $G_Λ,$ which is invariant under derived equivalences. We …
View article: Cokernels of the Cartan matrix and stratifying systems
Cokernels of the Cartan matrix and stratifying systems Open
We study the cokernel of the application given by the Cartan matrix CΛ of a finite dimensional k-algebra Λ. This produces a finitely generated abelian group, the Cartan group GΛ, which is invariant under derived equivalences. We are intere…
View article: A generalization of the theory of standardly stratified algebras I: Standardly stratified ringoids
A generalization of the theory of standardly stratified algebras I: Standardly stratified ringoids Open
We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental result…
View article: Wide subcategories of finitely generated Λ-modules
Wide subcategories of finitely generated Λ-modules Open
We explore some properties of wide subcategories of the category [Formula: see text] of finitely generated left [Formula: see text]-modules, for some artin algebra [Formula: see text] In particular we look at wide finitely generated subcat…
View article: Coherent subcategories of finitely generated $Λ$-modules
Coherent subcategories of finitely generated $Λ$-modules Open
We explore some properties of wide subcategories of the category mod$\,(Λ)$ of finitely generated left $Λ$-modules, for some artin algebra $Λ.$ In particular we look at wide finitely generated subcategories and give a connection with the c…
View article: Coherent subcategories of finitely generated $\Lambda$-modules
Coherent subcategories of finitely generated $\Lambda$-modules Open
We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a con…