We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–
Schmidt exact category 𝒞. This duality induces the generalized Auslander–Reiten …

For a length abelian category, we show that all torsion-free classes can be classified by
using only the information on bricks, including non functorially-finite ones. The idea is to …

Inspired by the recent work of Henrard, Kvamme and van Roosmalen [17], we prove a
categorified version of higher Auslander correspondence in the context of exact categories …

Let C be an (d+ 2)-angulated category with an d-suspension functor Σd. Our main results
show that every Serre functor on C is an (d+ 2)-angulated functor. We also show that C has a …

We review the basic definitions of derived categories and derived functors. We illustrate
them on simple but non trivial examples. Then we explain Happel's theorem which states …

In this paper we introduce a special kind of relative (co) resolutions associated to a pair of
classes of objects in an abelian category $\mathcal {C}. $ We will see that, by studying these …

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and extension-closed subcategories of triangulated …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

TILTING OBJECTS ON SOME GLOBAL QUOTIENT STACKS 1. Introduction. Geometric tilting
theory began with the con- struction of tiltin Page 1 JOURNAL OF COMMUTATIVE ALGEBRA …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …