Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product

The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. limit this procedure, called asymptotic product, provides a homological counterpart Buchweitz's construction stable cohomology. resulting connected sequence functors isomorphic Triulzi's J-completion Tor functor. A comparison map from Vogel homology constructed and shown be always epic. category finitely presented complete cocomplete. As consequence, inert with fixed variable generated module over artin algebra presented. Its defect consequently all right-derived are determined. New notions torsion cotorsion introduced related each other.