Related papers: An exact structure approach to almost rigid module…

We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the…

We consider representations of quivers taking values in monads or comonads over a Grothendieck category $\mathcal C$. We treat these as scheme like objects whose ``structure sheaf'' consists of monads or comonads. By using systems of…

This paper calculates the number of full exceptional collections modulo an action of a free abelian group of rank one for an abelian category of coherent sheaves on an orbifold projective line with a positive orbifold Euler characteristic,…

We introduce graded $\mathbb{E}_{\infty}$-rings and graded modules over them, and study their properties. We construct projective schemes associated to connective $\mathbb{N}$-graded $\mathbb{E}_{\infty}$-rings in spectral algebraic…

Examples of exact categories in representation theory are given by the category of Delta-filtered modules over quasi-hereditary algebras, but also by various categories related to matrix problems, such as poset representations or…

We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but does contain a pair of novel results. Over finite posets,…

We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in the categorical tilting context and beyond. In the $n$-tilting-cotilting correspondence situation, if $\mathsf A$ is a…

The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…

We introduce the notion of an exact dg category, which is a simultaneous generalization of the notions of exact category in the sense of Quillen and of pretriangulated dg category in the sense of Bondal--Kapranov. It is also a differential…

Cluster algebra structures for Grassmannians and their (open) positroid strata are controlled by a Postnikov diagram D or, equivalently, a dimer model on the disc, as encoded by either a bipartite graph or the dual quiver (with faces). The…

For an $(n-1)$-Auslander algebra $\Lambda$ with global dimension $n$, we give some necessary conditions for $\Lambda$ admitting a maximal $(n-1)$-orthogonal subcategory in terms of the properties of simple $\Lambda$-modules with projective…

In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of…

In this paper, we initiate the study of nondiagonal finite quasi-quantum groups over finite abelian groups. We mainly study the Nichols algebras in the twisted Yetter-Drinfeld module category $_{\k G}^{\k G}\mathcal{YD}^\Phi$ with $\Phi$ a…

We prove that the category of finitely generated graded modules over the quiver Hecke algebra of arbitrary type admits numerous stratifications in the sense of Kleshchev. A direct consequence is that the full subcategory corresponding to…

We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…

We continue our study of relatively divisible and relatively flat objects in exact categories in the sense of Quillen with several applications to exact structures on finitely accessible additive categories and module categories. We derive…

We present a new way to construct $n$-cluster tilting subcategories of abelian categories. Our method takes as input a direct system of abelian categories $\mathcal{A}_i$ with certain subcategories and, under reasonable conditions, outputs…

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a…

In this paper we study categories of tilting modules. Our starting point is the tilting modules for a reductive algebraic group G in positive characteristic. Here we extend the main result in [8] by proving that these tilting modules form a…

We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…