Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

Let $ R $ be a ring and $\mathsf S $ be a class of strongly finitely presented (FP ${} _\infty $)
$ R $-modules closed under extensions, direct summands, and syzygies. Let $(\mathsf …

In an arbitrary Grothendieck category, we find necessary and sufficient conditions for the
class of FP n-injective objects to be a torsion class. By doing so, we propose a notion of n …

We give sufficient conditions which ensure that a functor of finite length from an additive
category to finite-dimensional vector spaces has a projective resolution whose terms are …

In this paper, we introduce a class of exact structures in terms of finiteness conditions of
modules, which are called n-pure exact structures. We investigate the properties of n-pure …

In this paper we introduce a special kind of relative (co) resolutions associated to a pair of
classes of objects in an abelian category $\mathcal {C}. $ We will see that, by studying these …

We relate the notions of Noetherian, regular coherent and regular $ n $-coherent category
for $\mathbb {Z} $-linear categories with finite objects with the corresponding notions for …

We establish connections between the concepts of Noetherian, regular coherent, and
regular n-coherent categories for Z-linear categories with finitely many objects and the …

We present the concept of cotorsion pairs cut along subcategories of an abelian category.
This provides a generalization of complete cotorsion pairs, and represents a general …

Starting with a Grothendieck category G and a torsion pair t D. T; F/in G, we study the local
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten …