We give criteria for subcategories of a compactly generated algebraic triangulated category
to be precovering or preenveloping. These criteria are formulated in terms of closure …

Abstract Let (B, E, s) be an extriangulated category and S be an extension closed
subcategory of ℬ. In this article, we prove that the Gabriel-Zisman localization B/S can be …

Auslander-Reiten conjecture, which says that an Artin algebra does not have any non-
projective generator with vanishing self-extensions in all positive degrees, is shown to be …

Rickard proved that for certain self‐injective algebras, a stable equivalence induced from an
exact functor is a stable equivalence of Morita type, in the sense of Broué. In this paper we …

Abstract Let Q → RQ→ R be a surjective homomorphism of Noetherian rings such that Q is
Gorenstein and R as a Q-bimodule admits a finite resolution by modules which are …

We propose a solution to the''curvature problem''from arXiv: 1505.03698 and arXiv:
0905.3845 for infinitesimal deformations. Let $ k $ be a field, $ A $ a dg algebra over $ k …

The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …

A successful theme in the development of triangulated categories has been the study of
compact objects. A weak dual notion called 0-cocompact objects was introduced in …

We use Quillen model structures to show a systematic method to lift recollements of
hereditary abelian model categories to recollements of their associated homotopy …

We apply the Auslander–Buchweitz approximation theory to show that the Iyama and
Yoshino's subfactor triangulated category can be realized as a triangulated quotient …