Related papers: Recollements for dualizing $k$-varieties and Ausla…

Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor…

According to the Auslander's formula one way of studying an abelian category ${\mathcal{C}}$ is to study ${\rm mod}\mbox{-}{\mathcal{C}}$, that has nicer homological properties than ${\mathcal{C}}$, and then translate the results back to…

We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that…

For a nice-enough category $\mathcal{C}$, we construct both the morphism category ${\rm H}(\mathcal{C})$ of $\mathcal{C}$ and the category ${\rm mod}\mbox{-}\mathcal{C}$ of all finitely presented contravariant additive functors over…

Recently, Wang, Wei and Zhang introduced the notion of recollements of extriangulated categories. In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. We provide some methods to construct…

The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ of admissibly finitely presented functors and use it to give a version…

Let $R$ be a commutative artinian ring. We extend higher Auslander correspondence from Artin $R$-algebras of finite representation type to dualizing $R$-varieties. More precisely, for a positive integer $d$, we show that a dualizing…

Auslander's formula shows that any abelian category C is equivalent to the category of coherent functors on C modulo the Serre subcategory of all effaceable functors. We establish a derived version of this equivalence. This amounts to…

We characterize the generalized Auslander--Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite…

In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by…

A recollement of triangulated categories describes one such category as being "glued together" from two others. This paper gives a precise criterion for the existence of a recollement of the derived category of a Differential Graded Algebra…

We prove Auslander's defect formula in an exact category, and obtain a commutative triangle involving the Auslander bijections and the generalized Auslander-Reiten duality.

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…

Using the Nakayama duality induced by a Nakayama functor, we provide a novel and concise account of the existence of Auslander-Reiten dualities and almost split sequences in abelian categories with enough projective objects or enough…

In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…

In this paper we continue the study of triangular matrix categories $\mathbf{\Lambda}=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$ initiated in [21]. First, given an additive category $\mathcal{C}$…

Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors $mod$-$\mathcal{M}$ modulo the subcategory of effaceable functors $mod_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory which…

nspired by the work of J$\o$rgensen [J], we define a (upper-, lower-) symmetric recollements; and give a one-one correspondence between the equivalent classes of the upper-symmetric recollements and one of the lower-symmetric recollements,…

In this paper we investigate equivariant recollements of abelian (resp. triangulated) categories. We first characterize when a recollement of abelian (resp. triangulated) categories induces an equivariant recollement, i.e. a recollement…

We study connections between recollements of the derived category D(Mod-R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature.…