Related papers: Tilting subcategories in extriangulated categories

Let $\mathscr{C}$ be an $n$-exangulated category. In this note, we show that if $\mathscr{C}$ is locally finite, then $\mathscr{C}$ has Auslander-Reiten $n$-exangles. This unifies and extends results of Xiao-Zhu, Zhu-Zhuang, Zhou and…

We construct two functors from the submodule category of a self-injective representation-finite algebra $\Lambda$ to the module category of the stable Auslander algebra of $\Lambda$. These functors factor through the module category of the…

A subcategory $\mathscr{W}$ of an abelian category is called wide if it is closed under kernels, cokernels, and extensions. Wide subcategories are of interest in representation theory because of their links to other homological and…

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…

We show that the Verdier quotients can be realized as subfactors by the homotopy theory of additive categories with suspensions developed in \cite{ZWLi2, ZWLi3}. As applications, we develop the homotopy theory of Nakaoka twin cotorsion…

We give a complete classification of torsion pairs in repetitive cluster categories of type $A_n$, which were defined by Zhu as the orbit categories, via certain configurations of diagonals, called Ptolemy diagrams. As applications, we…

We give a characterization of radical square zero bound quiver algebras $\mathbf{k} Q/\mathcal{J}^2$ that admit $n$-cluster tilting subcategories and $n\mathbb{Z}$-cluster tilting subcategories in terms of $Q$. We also show that if $Q$ is…

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…

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…

We study ideal cotorsion pairs associated to weak proper classes of triangles in extension closed subcategories of triangulated categories. This approach allows us to extend the recent ideal approximations theory developed by Fu, Herzog et…

Herschend-Liu-Nakaoka introduced the concept of $n$-exangulated categories as higher-dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact categories and…

Cluster algebras are categorified by cluster categories, and $g$-vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently introduced completed discrete cluster categories of Dynkin…

Cluster categories were introduced in 2006 by Buan-Marsh-Reineke-Reiten-Todorov in order to categorify acyclic cluster algebras without coefficients. Their construction was generalized by Amiot (2009) and Plamondon (2011) to arbitrary…

The basic properties of locally finite triangulated categories are discussed. The focus is on Auslander--Reiten theory and the lattice of thick subcategories.

Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic characterisations of when such categories have a natural extriangulated structure and are appearing as…

We provide an explicit procedure to glue (not necessarily compact) silting objects along recollements of triangulated categories with coproducts having a 'nice' set of generators, namely, well generated triangulated categories. This…

Let $\Lambda$ be a finite-dimensional basic algebra. Sakai recently used certain sequences of image-cokernel-extension-closed (ICE-closed) subcategories of finitely generated $\Lambda$-modules to classify certain (generalized) intermediate…

Let $\mathscr{C}$ be a 2-Calabi-Yau triangulated category, and let $\mathscr{T}$ be a cluster tilting subcategory of $\mathscr{C}$. An important result from Dehy and Keller tells us that a rigid object $c \in \mathscr{C}$ is uniquely…

In this paper we develop a graded tilting theory for gauged Landau-Ginzburg models of regular sections in vector bundles over projective varieties. Our main theoretical result describes - under certain conditions - the bounded derived…

In a compactly generated triangulated category, we introduce a class of tilting objects satisfying certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent…