Tilting theory has been a very important tool in the classification of finite dimensional
algebras of finite and tame representation type, as well as, in many other branches of …

For a triangulated category TT, if CC is a cluster-tilting subcategory of TT, then the factor
category T/CT/C is an abelian category. Under certain conditions, the converse also holds …

In this paper, we investigate the homological properties of the functor categories (mod− R,
Ab) and ((mod− R) op, Ab). Some new homological dimensions in these functor categories …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

For a triangulated category C with a cluster tilting subcategory T which contains infinitely
many indecomposable objects, the notion of weak T [1]-cluster tilting subcategories of C is …

Let (C, E, s) be an extriangulated category. We show that certain quotient categories of
extriangulated categories are equivalent to module categories by some restriction of functor …

In this article, we introduce the notion of {\it concentric twin cotorsion pair} on a triangulated
category. This notion contains the notions of $ t $-structure, cluster tilting subcategory, co-$ t …

We introduce the notions of silting comodules and finitely silting comodules in quasi-finite
category, and study some properties of them. We investigate the torsion pair and dualities …