In this paper, we study (complete) cotorsion pairs in extriangulated categories. First, we
study a relationship between an interval of the poset of cotorsion pairs and the poset of …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type FP n and studying their closure properties with respect to short exact …

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 …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …

In this work we introduce notions in Auslander-Buchweitz theory and cotorsion theory in
extriangulated categories which extend the given ones for abelian categories. Although …

Let $ R $ be a Ding-Chen ring. Yang\cite {Yang2012} and Zhang\cite {Zhang2015} asked
whether or not every $ R $-module has finite Ding projective or Ding injective dimension. In …

In this paper we study a generalisation of the Igusa-Todorov functions which gives rise to a
vast class of algebras satisfying the finitistic dimension conjecture. This class of algebras is …

In this paper we study the finiteness of global Gorenstein AC-homological dimensions for
rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an …

Given a Frobenius pair in a module category, we describe how to construct Frobenius pairs
in some other important abelian categories, such as the category of complexes of modules …