Limit Koszul cohomology and torsion theory

The new notion of filter set is introduced in this article. We define a Koszul complex with respect to filter set and we consider the generalized limit cohomology functors. The construction generalized a number of earlier theories under review. We consider the connections between limit Koszul cohomology functors and local cohomology functors and generalized local cohomology functors of J. Herzog–Bijan-Zadeh.