We give a full classification of representation types of the subcategories of representations of
an m× n rectangular grid with monomorphisms (dually, epimorphisms) in one or both …

The main theme of this paper is to study $\tau $-tilting subcategories in an abelian category
$\mathscr {A} $ with enough projective objects. We introduce the notion of $\tau $-cotorsion …

Let T be a right exact functor from an abelian category ℬ into another abelian category A.
Then there exists a functor p from the product category A× ℬ to the comma category ((T↓ …

Balanced pairs appear naturally in the realm of relative homological algebra associated with
the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural …

Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M 0 & B\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. Given two complete hereditary …

We study Gorenstein flat objects in the category Rep (Q, R) of representations of a left rooted
quiver Q with values in Mod (R), the category of all left R-modules, where R is an arbitrary …

The 𝑄-shaped derived category of a ring — compact and perfect objects Page 1
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 377, Number 5 …

Given a complete hereditary cotorsion pair (A, B) in an abelian category C satisfying certain
conditions, we study the completeness of the induced cotorsion pairs (Φ (A), Φ (A)⊥) and …

We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

We investigate the (separated) monomorphism category $\operatorname
{mono}(Q,\Lambda) $ of a quiver $ Q $ over an Artin algebra $\Lambda $. We construct an …