Recently a notion of support and a construction of local cohomology functors for [TR5]
compactly generated triangulated categories were introduced and studied by Benson …

Given an exact functor between triangulated categories which admits both adjoints and
whose cotwist is either zero or an autoequivalence, we show how to associate a unique full …

The local structure of homomorphisms of commutative noetherian rings is investigated from
the point of view of dualizing complexes. A concept of finite Gorenstein dimension, which …

We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

Let $ k $ be a commutative ring, let ${\mathcal {C}} $ be a small, $ k $-linear, Hom-finite,
locally bounded category, and let ${\mathcal {B}} $ be a $ k $-linear abelian category. We …

We study the homotopy category of unbounded complexes of Gorenstein-projective
modules with bounded relative homologies. We show the existence of a right recollement of …

Abstract Let AA and BB be abelian categories and F: A → BF: A→ B an additive and right
exact functor which is perfect, and let (F, B)(F, B) be the left comma category. We give an …

In this work we construct a compactly generated tensor-triangulated stable category for a
large class of infinite groups, including those in Kropholler's hierarchy $\mathrm …

Let 𝒜 be an abelian category and 𝒳, 𝒴, 𝒵 additive full subcategories of 𝒜. We introduce and
study the Gorenstein category 𝒢 (𝒳, 𝒴, 𝒵) as a common generalization of some known …

We investigate the problem when the tensor functor by a bimodule yields a singular
equivalence. It turns out that this problem is equivalent to the one when the Hom functor …