Abstract We revisit Auslander–Buchweitz approximation theory and find some relations with
cotorsion pairs and model category structures. From the notion of relative generators, we …

We give a representation-theoretic bijection between rooted labeled forests with $ n $
vertices and complete exceptional sequences for the quiver of type $ A_n $ with straight …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

arXiv:1904.11903v2 [math.RT] 27 May 2020 Page 1 arXiv:1904.11903v2 [math.RT] 27 May
2020 STRATIFYING SYSTEMS THROUGH τ-TILTING THEORY OCTAVIO MENDOZA AND …

Let R be a finite dimensional k-algebra over an algebraically closed field k and modR be the
category of all finitely generated left R-modules. For a given full subcategory X of modR, we …

We introduce and develop an analogous of the Auslander–Buchweitz approximation theory
(see Auslander and Buchweitz, Societe Mathematique de France 38: 5–37, 1989) in the …

We introduce the so-called homological systems in a module category over a pre-ordered
set, which generalize the notion of a stratifying system over a linearly ordered set, and study …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

In this article, we define relative resolutions and coresolutions in extriangulated categories.
By studying this relative resolutions and coresolutions, we get a generalization of the …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …