Let $ T_R $ be a right $ n $-tilting module over an arbitrary associative ring $ R $. In this
paper we prove that there exists an $ n $-tilting module $ T'_R $ equivalent to $ T_R $ which …

We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–
Schmidt exact category 𝒞. This duality induces the generalized Auslander–Reiten …

Let 𝒞 be a triangulated category. When ω is a functorially finite subcategory of 𝒞, Jøtrgensen
showed that the stable category 𝒞/ω is a pretriangulated category. A pair (𝒳, 𝒴) of …

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 …

In our previous article, we constructed an abelian category from any torsion pair on a
triangulated category. This generalizes the heart of a t-structure and the ideal quotient by a …

This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-
Yau triangulated categories. Let 𝓒 be a 2-Calabi-Yau triangulated category with suspension …

We define the notion of an infinitely generated tilting object of infinite homological dimension
in an abelian category. A one-to-one correspondence between∞-tilting objects in complete …

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 …

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 prove a generalization to the context of topological tilting modules of the fact that a tilting
module is faithfully balanced and also a tilting module over its endomorphism ring. Some …