In this paper the authors investigate homological and homotopical aspects of a concept of
torsion which is general enough to cover torsion and cotorsion pairs in abelian categories …

1. Introduction. 2. Proper classes of triangles and phantom maps. 3. The Steenrod and Freyd
category of a triangulated category. 4. Projectie objects, resolutions, and deried functors. 5 …

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

Let C be an abelian or exact category with enough projectives and let P be the full
subcategory of projective objects of C. We consider the stable category C/P modulo …

We study Artin algebras Λ and commutative Noetherian complete local rings R in connection
with the following decomposition property of Gorenstein-projective modules: We show that …

We develop some aspects of the theory of derivators, pointed derivators and stable
derivators. Stable derivators are shown to canonically take values in triangulated categories …

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

To any additive category, we associate in a functorial way two additive categories A (), B ().
The category A (), resp. B (), is the reflection of in the category of additive categories with …

For an exact category EE with enough projectives and with ad Z d Z-cluster tilting
subcategory, we show that the singularity category of EE admits ad Z d Z-cluster tilting …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …