The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

Extriangulated categories were introduced by Nakaoka and Palu by extracting the
similarities between exact categories and triangulated categories. A notion of mutation of …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …

Let A be a finite dimensional algebra over an algebraically closed field k. Suppose that the
Auslander-Reiten quiver r of A is finite and contains no oriented cycles, Let S be a simple A …

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 …

We show that the category of orbits of the bounded derived category of a hereditary category
under a well-behaved autoequivalence is canonically triangulated. This answers a question …

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and triangulated categories. We consider in this article the …

A k-linear triangulated category A is called locally finite provided∑ X∈ indAdimkHomA (X,
Y)<∞ for any indecomposable object Y in A. It has Auslander–Reiten triangles. In this paper …

Report on locally finite triangulated categories Page 1 J. K-Theory 9 (2012), 421–458 doi:10.1017/is011011005jkt172
©2011 ISOPP Report on locally finite triangulated categories by HENNING KRAUSE …

A class of triangulated categories with a finiteness condition is singled out. These
triangulated categories have Auslander–Reiten triangles. It is proved that the relations of the …