Category theory was introduced in the early 1940s by Eilenberg and MacLane [48, 49].
Since Grothendieck [81] succeeded in applying category theory to the study of algebraic …

We classify compactly generated co-$ t $-structures on the derived category of a
commutative noetherian ring. In order to accomplish this, we develop a theory for compactly …

We study the inverse problem of constructing in a natural way a ring S and such a
homomorphism, from an abstract algebraic closure operator C on finitely generated free R …

An abelian category with arbitrary coproducts and a small projective generator is equivalent
to a module category (Mitchell (1964)[17]). A tilting object in an abelian category is a natural …

The aim of this paper is to develop a framework for localization theory of triangulated
categories\(\mathcal {C}\), that is, from a given extension-closed subcategory\(\mathcal {N}\) …

Consider a monad on an idempotent complete triangulated category with the property that
its Eilenberg–Moore category of modules inherits a triangulation. We show that any other …

The representation theory of a ring Δ has been studied by examining the category of
contravariant (additive) functors from the category of finitely generated left Δ-modules to the …

We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

In finitely cocomplete homological categories, co-smash products give rise to (possibly
higher-order) commutators of subobjects. We use binary and ternary co-smash products and …

The purpose of this paper is to indicate that most of noncommutative homological ring theory
generalizes to (pre) additive category theory, as well as to provide some reasons for wanting …