Related papers: Stable categories and reconstruction

From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…

Starting from a (small) rigid C$^*$-tensor category $\mathscr{C}$ with simple unit, we construct von Neumann algebras associated to each of its objects. These algebras are factors and can be either semifinite (of type II$_1$ or II$_\infty$,…

We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We…

We show that if two $m$-homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalence between the categories of comodules for their associated…

In this short \'etude, we observe that the full structure of a recollement on a stable infinity-category can be reconstructed from minimal data: that of a reflective and coreflective full subcategory. The situation has more symmetry than…

Stable equivalences of Morita type preserve many interesting properties and is proved to be the appropriate concept to study for equivalences between stable categories. Recently the singularity category attained much attraction and Xiao-Wu…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

For any ring R we construct two triangulated categories, each admitting a functor from R-modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or Gorenstein ring, these triangulated categories agree with each…

Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra $A$ we associate a triple $(\Sigma_A, \Lambda_A; \eta_A)$, where $\Sigma_A$ is an oriented smooth surface with…

A.S. Dugas and R. Mart\'{i}nez-Villa proved in \cite[Corollary 5.1]{dm} that if there exists a stable equivalence of Morita type between the $k$-algebras $\Lambda$ and $\Gamma$, then it is possible to replace $\Lambda$ by a Morita…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

We construct Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This is a continuation of our earlier work where we established…

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…

Let $\X$ be a resolving subcategory of an abelian category. In this paper we investigate the singularity category $\ds(\underline\X)=\db(\mod\underline\X)/\kb(\proj(\mod\underline\X))$ of the stable category $\underline\X$ of $\X$. We…

We prove that for any $\mathbb{N}$-graded Gorenstein tiled order $A$, the stable category $\underline{\mathrm{CM}}^{\mathbb{Z}}A$ is triangle equivalent to the perfect derived category of the incidence algebra of a finite poset…

We investigate the stabilization $\mathcal{S}$ of the module category over an artinian ring $\Lambda$ by formally inverting the tensor endofunctor given by the bimodule of relative noncommutative differential $1$-forms. It turns out that…

We describe the class of semi-stable model categories, which generalize the equivalence of finite products and coproducts in abelian and stable model categories, and use this to establish Morita equivalences among categories of functors. We…

Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories…

Let $\Lambda$ be an arbitrary monomial algebra. We investigate the stable category $\underline{\operatorname{Gproj}}^{\mathbb{Z}}\Lambda$ of graded Gorenstein-projective $\Lambda$-modules and the orbit category…

It is well-known that the Steenrod algebra $A$ is self-injective as a graded ring. We make the observation that simply changing the grading on $A$ can make it cease to be self-injective. We see also that $A$ is not self-injective as an…