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 …

Let Φ be a finite dimensional algebra over an algebraically closed field k and assume gldim
Φ≤ d, for some fixed positive integer d. For d= 1, Brüning proved that there is a bijection …

This paper studies Auslander-Reiten triangles in subcategories of triangulated categories.
The main theorem shows that the Auslander-Reiten triangles in a subcategory are closely …

Auslander-Reiten triangles and quivers are introduced into algebraic topology. It is proved
that the existence of Auslander-Reiten triangles characterizes Poincaré duality spaces, and …

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 …

This paper deals with the representation theory of strongly, locally finite quivers. We first
study some properties of the finitely presented or co‐presented representations, and then …

The Auslander–Reiten formula for complexes of modules Page 1 Advances in Mathematics 207
(2006) 133–148 www.elsevier.com/locate/aim The Auslander–Reiten formula for complexes …

When the base connected cochain DG algebra is cohomologically bounded, it is proved that
the difference between the amplitude of a compact DG module and that of the DG algebra is …

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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 …