Related papers: Recollements and $n$-cotorsion pairs

We study a structure of subcategories which are called a polygon of recollements in a triangulated category. First, we study a $2n$-gon of recollements in an $(m/n)$-Calabi-Yau triangulated category. Second, we show the homotopy category…

Let $\mathcal{B}$ be an abelian category with enough projective objects and enough injective objects and let $\mathcal{A}=\mathcal{B}\ltimes_\eta\mathsf{F}$ be an $\eta$-extension of $\mathcal{B}$. Given a cotorsion pair…

We develop the theory of recollements in a stable $\infty$-categorical setting. In the axiomatization of Beilinson, Bernstein and Deligne, recollement situations provide a generalization of Grothendieck's "six functors" between derived…

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…

In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements…

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…

In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a…

Given a right exact functor from an abelian category into another abelian category, there is an associated abelian category called the comma category of the functor. In this paper, we characterize when left Frobenius pairs (resp. strong…

Hovey's correspondence between model structures and cotorsion pairs in the setting of abelian categories, has been generalized by Nakaoka-Palu, using two cotorsion pairs, to the setting of weakly idempotent complete extriangulated…

Given a complete hereditary cotorsion pair $(\mathcal{A},\mathcal{B})$ in a Grothendieck category $\mathcal{G}$, the derived category $\mathcal{D}(\mathcal{B})$ of the exact category $\mathcal{B}$ is defined as the quotient of the category…

In this paper, we study the relationship of Gorenstein projective objects among three Abelian categories in a recollement. As an application, we introduce the relation of $n$-Gorenstein tilting modules (and Gorenstein syzygy modules) in…

In this article we construct various models for singularity categories of modules over differential graded rings. The main technique is the connection between abelian model structures, cotorsion pairs and deconstructible classes, and our…

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 $\C$.…

Let $\mathcal B$ be an extriangulated category with enough projectives and enough injectives. We define a proper $m$-term subcategory $\mathcal G$ on $\mathcal B$, which is an extriangulated subcategory. Then we give a correspondence…

We use Quillen model structures to show a systematic method to lift recollements of hereditary abelian model categories to recollements of their associated homotopy categories. To that end, we use the notion of Quillen adjoint triples and…

Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity…

In the paper "Cotorsion Pairs in C(R-Mod)", the authors construct an abelian model structure on the category of chain complexes Ch(R), where the class of cofibrant objects is given by the class of degreewise projective chain complexes.…

This is the second paper in a series on representations over diagrams of abelian categories. We show that, under certain conditions, a compatible family of abelian model categories indexed by a skeletal small category can be amalgamated…

In this article, we introduce the notion of {\it concentric twin cotorsion pair} on a triangulated category. This notion contains the notions of $t$-structure, cluster tilting subcategory, co-$t$-structure and functorally finite rigid…

Let $(\mbox{mod} \Lambda',\mbox{mod} \Lambda,\mbox{mod} \Lambda'')$ be a recollement of module categories for artin algebras $\Lambda'$, $\Lambda$ and $\Lambda''$. We provide a sufficient condition such that a glued torsion pair in…