7 papers
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…
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 high…
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{\operatornam…
The left heart and exact hull of an additive regular category
Ruben Henrard, Sondre Kvamme, Adam-Christiaan van Roosmalen +1
Quasi-abelian categories are abundant in functional analysis and representation theory. It is known that a quasi-abelian category is a cotilting torsionfree class of…
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…
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…