Generalized Tate cohomology and Avramov–Martsinkovsky type sequences

Abstract

Let [Formula: see text] be an abelian category with enough projectives. In the category of [Formula: see text]-complexes, we introduce generalized Tate cohomology with respect to subcategories, and show that there is an Avramov–Martsinkovsky type exact sequence connecting the absolute cohomology, relative cohomology and generalized Tate cohomology.