Abstract We study Gorenstein categories. We show that such a category has Tate
cohomological functors and Avramov–Martsinkovsky exact sequences connecting the …

We investigate Tate cohomology of modules over a commutative noetherian ring with
respect to semidualizing modules. We identify classes of modules admitting Tate resolutions …

Let 𝒜 be an abelian category with enough projectives. In the category of 𝒜-complexes, we
introduce generalized Tate cohomology with respect to subcategories, and show that there …

Gorenstein homological algebra was introduced in categories of modules. But it has proved
to be a fruitful way to study various other categories such as categories of complexes and of …

We compare relative cohomology theories arising from using different proper resolutions of
modules. Criteria for the vanishing of such distinctions are given in certain cases, and we …

Based on the analysis of Tate and generalized Tate cohomology in abelian categories, in
this note, we consider the balance for Tate and generalized Tate cohomology. Some …