40 citations · 115 across the 13 of their papers we have counts for
13 papers · 1 filter
Higher torsion classes, -tilting theory and silting complexes
Jenny August, Johanne Haugland, Karin M. Jacobsen +3
Initiated in work by Adachi, Iyama and Reiten, the area known as -tilting theory plays a fundamental role in contemporary representation theory. In this paper we explore a highe…
Higher extension closure and -exact categories
Sondre Kvamme
We prove that any weakly idempotent complete -exact category is equivalent to a -cluster tilting subcategory of a weakly idempotent complete exact category, and that any weak…
An introduction to monomorphism categories
Sondre Kvamme
This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be divided into four parts: The first part is an introduction to the theory of monomorphism…
A functorial approach to monomorphism categories II: Indecomposables
Nan Gao, Julian Külshammer, Sondre Kvamme +1
We investigate the (separated) monomorphism category of a quiver over an Artin algebra . We construct an epivalence from $\overline{\operatorname{…
A characterisation of higher torsion classes
Jenny August, Johanne Haugland, Karin M. Jacobsen +3
Let be an abelian length category containing a -cluster tilting subcategory . We prove that a subcategory of is a -torsion class if a…
-cluster tilting subcategories for Nakayama algebras
Martin Herschend, Sondre Kvamme, Laertis Vaso
-cluster tilting subcategories are an ideal setting for higher dimensional Auslander-Reiten theory. We give a complete classification of -cluster tilting…
Auslander's formula and correspondence for exact categories
Ruben Henrard, Sondre Kvamme, Adam-Christiaan van Roosmalen
The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category of admissi…
Axiomatizing Subcategories of Abelian Categories
Sondre Kvamme
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find intrinsic axioms which characterize generating cogenerat…
A functorial approach to monomorphism categories for species I
Nan Gao, Julian Külshammer, Sondre Kvamme +1
We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalised species over locally bounded quivers.…
-cluster tilting subcategories of singularity categories
Sondre Kvamme
For an exact category with enough projectives and with a -cluster tilting subcategory, we show that the singularity category of admits a $d…
Co-Gorenstein algebras
Sondre Kvamme, Rene Marczinzik
We review the theory of Co-Gorenstein algebras, which was introduced by Beligiannis in the article "The Homological Theory of Contravariantly Finite Subcategories: Gorenstein Categ…
An introduction to higher Auslander-Reiten theory
Gustavo Jasso, Sondre Kvamme
This article consists of an introduction to Iyama's higher Auslander-Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proof…
Higher Nakayama algebras I: Construction
Gustavo Jasso, Julian Külshammer
We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander--Reiten theory. More precisely, for each Nakayama algebra and…