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 introduce a relative tilting theory in abelian categories and show that this work offers a
unified framework of different previous notions of tilting, ranging from Auslander-Solberg …

Suppose that $\mathcal {A} $ is an abelian category whose derived category $\mathcal
{D}(\mathcal {A}) $ has $ Hom $ sets and arbitrary (small) coproducts, let $ T $ be a (not …

We introduce a relative tilting theory in abelian categories and show that this work offers a
unified framework of different previous notions of tilting, ranging from Auslander-Solberg …

We study ideal cotorsion pairs associated to almost exact structures in extension closed
subcategories of triangulated categories. This approach allows us to extend the recent ideal …

In this paper, we study the ideal approximation theory associated to almost $ n $-exact
structures in the $ n $-exangulated category. The notions of $ n $-ideal cotorsion pairs and …

We give a category theoretic approach to several known equivalences from (classic) tilting
theory and commutative algebra. Furthermore, we apply our main results to establish a …

For a small abelian category C, Auslander's formula allows us to express C as a quotient of
the category mod− C of coherent functors on C. We consider an abelian category with the …

We study ideal cotorsion pairs associated to weak proper classes of triangles in extension
closed subcategories of triangulated categories. This approach allows us to extend the …

Let $\mathcal {A} $ be a Hom-finite abelian category with enough projectives. In this note,
we show that any covariantly finite $\tau $-rigid subcategory is contained in a support $\tau …