Related papers: Hereditary cotorsion pairs on extriangulated subca…

We study the category $\mathrm{Rep}(Q,\mathcal{M})$ of representations of a quiver $Q$ with values in an abelian category $\mathcal{M}$. Under certain assumptions, we show that every cotorsion pair $(\mathcal{A},\mathcal{B})$ in…

Let $\mathcal{E}=(\mathcal{A},\mathcal{S})$ be an exact category with enough projectives $\mathcal{P}$. We introduce the notion of support $\tau$-tilting subcategories of $\mathcal{E}$. It is compatible with existing definitions of support…

Let $\mathcal A$ be a Hom-finite abelian category with enough projectives. In this note, we show that any covariantly finite $\tau$-rigid subcategory is contained in a support $\tau$-tilting subcategory. We also show that support…

In this article, we study the Gorenstein property of abelian quotient categories induced by fully rigid subcategories on an exact category B. We also study when d-cluster tilting subcategories become fully rigid. We show that the quotient…

We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain…

In this paper, we first construct some complete cotorson pairs on the category $\mathbb{C}_N(\mathcal{G})$ of unbounded $N$-complexes of Grothendieck category $\mathcal{G}$, from two given cotorsion pairs in $\mathcal{G}$. Next as an…

We call a triangulated category \emph{hereditary} provided that it is equivalent to the bounded derived category of a hereditary abelian category, where the equivalence is required to commute with the translation functors. If the…

We give necessary and sufficient conditions for torsion pairs in a hereditary category to be in bijection with $t$-structures in the bounded derived category of that hereditary category. We prove that the existence of a split $t$-structure…

Nakaoka and Palu introduced the notion of extriangulated categories by extracting the similarities between exact categories and triangulated categories. In this paper, we study cotorsion pairs in a Frobenius extriangulated category $\C$.…

For a recollement $(\mathcal{A},\mathcal{B},\mathcal{C})$ of abelian categories, we show that torsion pairs in $\mathcal{A}$ and $\mathcal{C}$ can induce torsion pairs in $\mathcal{B}$; and the converse holds true under certain conditions.

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas. To a torsion pair in the category $ R\operatorname{-}\operatorname{mod}$ of finitely presented modules over a left artinian ring $R$, we assign two…

Let $\mathcal{A}$ be an abelian category and $\mathcal{B}$ be the Happel-Reiten-Smal{\o} tilt of $\mathcal{A}$ with respect to a torsion pair. We give necessary and sufficient conditions for the existence of a derived equivalence between…

We give a simultaneous generalization of recollements of abelian categories and triangulated categories, which we call recollements of extriangulated categories. For a recollement $(\mathcal{A}$, $\mathcal{B}$, $\mathcal{C})$ of…

In this paper we introduce a special kind of relative (co)resolutions associated to a pair of classes of objects in an abelian category $\mathcal{C}.$ We will see that, by studying these relative (co)resolutions, we get a possible…

For any ring $R$, we investigate balanced pairs of classes of modules and their relations to cotorsion triples. We characterize the case when a balanced pair generates a tilting cotorsion pair, and dually, when it cogenerates a cotilting…

We introduce extriangulated factorization systems in extriangulated categories and show that there exists a bijection between $s$-torsion pairs and extriangulated factorization systems. We also consider the gluing of $s$-torsion pairs and…

Let $\mathcal C$ be a $(d+2)$-angulated category. In this paper, we define the notions of cotorsion pairs and weak cotorsion pairs in $\mathcal C$, which are generalizations of the classical cotorsion pairs in triangulated categories. As an…

In this paper we extend several classical results on pointed torsion theories -- also known as torsion pairs -- to the setting of non-pointed torsion theories defined via kernels and cokernels relative to a fixed class of trivial objects…

The notion of a pseudo cluster tilting subcategory $\mathcal X$ in an extriangulated category $\mathcal C$ is defined in this article. We prove that the quotient category $\mathcal C/\mathcal X$, obtained by factoring an extriangulated…

We study the category $\operatorname{Rep}(Q,\mathcal{C})$ of representations of a quiver $Q$ with values in an abelian category $\mathcal{C}$. For this purpose we introduce the mesh and the cone-shape cardinal numbers associated to the…