Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …

For a suitable triangulated category 𝒯 with a Serre functor S and a full precovering
subcategory 𝒞 closed under summands and extensions, an indecomposable object C in 𝒞 …

In this article, we prove a similar theorem to C, Theorem 6 which holds in a more general
setting. In particular, we focus on the construction of a natural morphism giving rise to a …

Socle-projective categories seem to be a link between the representation theory of modules
over finite dimensional algebras or artin algebras and other topics in representation theory …

For a length abelian category, we show that all torsion-free classes can be classified by
using only the information on bricks, including non functorially-finite ones. The idea is to …

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 …

We give a reduction theorem for silting intervals in extriangulated categories, which we call"
silting interval reduction".%{In triangulated categories, it generalizes Pauksztello …

We prove that an object U in a triangulated category with coproducts is silting if and only if it
is a (weak) generator of the category, the orthogonal class U⊥> 0 contains U, and U⊥> 0 is …

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 …