An Artin algebra is by definition virtually Gorenstein if the class of modules which are right
orthogonal (with respect to $\operatorname {Ext}^*(-,-) $) to all Gorenstein projective …

We prove that some subquotient categories of exact categories are abelian. This
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …

The notion of quotient and localization of abelian categories by dense subcategories (ie,
Serre classes) was introduced by Gabriel, and plays an important role in ring theory [6, 131 …

Let $\Lambda $ be an artin algebra or, more generally, a locally bounded associative
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …

If H is a hereditary abelian category with tilting object, then it is shown that H is derived
equivalent to a module category over a hereditary artin algebra provided H contains a …

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 …

Let $ A $ be a finite-dimensional algebra. The category $ bmod A $ of finitely generated left
$ A $-modules canonically embeds into the derived category ${D^ b}\left (A\right) $ of …

For self-injective algebras, Rickard proved that each derived equivalence induces a stable
equivalence of Morita type. For general algebras, it is unknown when a derived equivalence …

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

We show that an abelian category can be exactly, fully faithfully embedded into a module
category as the right perpendicular subcategory to a set of modules or module morphisms if …