Relative cotilting modules and their connection to ordinary cotilting modules were first
studied by Auslander and Solberg in [6] and [7]. Among other things, they show that relative …

It is proved that any tilting adjunction is completely described by an exact category with a
coherence property and the closure condition that exact sequences are acyclic. The …

Given two ringsRandS, we study the category equivalences T⇄ Y, where T is a torsion class
ofR-modules and Y is a torsion-free class ofS-modules. These equivalences correspond to …

Let G be a Grothendieck category, let t=(T, F) be a torsion pair in G and let (U t, W t) be the
associated Happel–Reiten–Smalø t-structure in the derived category D (G). We prove that …

Let T be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism
algebra Γ. Consider the functor T (T,−): T→ mod Γ. It induces a bijection from the …

Let M be a module over an associative ring R and σ [M] the category of M-subgenerated
modules. Generalizing the notion of a projective generator in σ [M], a module P∈ σ [M] is …

We show that the category of finite dimensional modules over the endomorphism algebra of
a rigid object in a Hom-finite triangulated category is equivalent to the Gabriel-Zisman …

Higher homological algebra was introduced by Iyama. It is also known as-homological
algebra where is a fixed integer, and it deals with-cluster tilting subcategories of abelian …

In his work [26], SE Dickson defined the notion of torsion theory (now called torsion pair) in
the general framework of abelian categories, which generalizes the concept of …

Assume that D is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor and a
cluster-tilting object T. We introduce the notion of ghost-tilting objects, and T [1]-tilting objects …