Related papers: From subcategories to the entire module categories

In this paper we show that the (un)bounded derived categories$\colon$(i) of the monomorphism category, (ii) of the morphism category and (iii) of the double morphism category, admit a periodic infinite ladder of recollements. These results…

Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…

We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to…

For $p$ a prime number and $\mathscr{P}$ a $p$-equipped finite partially ordered set we construct two different right-peak algebras (in the sense of \cite{KS}) $\Lambda^{(r)}$ and $\Lambda^{(c)}$. We consider the category…

We prove that algebras are left weakly Gorenstein in case the subcategory $^{\perp}A \cap \Omega^n(A)$ is representation-finite. This applies in particular to all monomial algebras and endomorphism algebras of modules over…

In a k-linear triangulated category (where k is a field) we show that the existence of Auslander-Reiten triangles implies that objects are determined, up to shift, by knowing dimensions of homomorphisms between them. In most cases the…

We prove that a finite dimensional algebra $A$ with representation-finite subcategory consisting of modules that are semi-Gorenstein-projective and $n$-th syzygy modules is left weakly Gorenstein. This generalises a theorem of Ringel and…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations…

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…

For a finite dimensional algebra $\Lambda$ and a non-negative integer $n$, we characterize when the set $\tilt_n\Lambda$ of additive equivalence classes of tilting modules with projective dimension at most $n$ has a minimal (or…

We define a type B analogue of the category of finite sets with surjections, and we study the representation theory of this category. We show that the opposite category is quasi-Grobner, which implies that submodules of finitely generated…

This paper deals with the representation theory of a locally finite quiver in which the number of paths between any two given vertices is finite. We first study some properties of the finitely presented or co-presented representations, and…

Let $\Lambda$ be an artin algebra. The aim of this paper is to outline a strong relationship between the Gabriel-Roiter inclusions and the Auslander-Reiten theory. If $X$ is a Gabriel-Roiter submodule of $Y,$ then $Y$ is shown to be a…

Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…

Let $\mathcal{X}$ be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over $\mathcal{X}$, we give a new and simple characterization of definable…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

We consider hereditary Artin algebras over arbitrary fields and prove that there is a natural bijection between the Weyl groups and the sets of full additive cofinite submodule closed subcategories of the module categories. While Oppermann,…

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic properties. We also introduce mixed (pre)cluster tilting…