In this paper we prove the conjectured isomorphism between stable K -theory and topological Hochschild homology over an arbitrary associative ring R , with coefficients in a bifunctor of finite degree in both variables. This work uses a purely algebraic approach and extends some classical constructions from the homology of groups to the case of the homology of a small category (which is isomorphic to topological Hochschild homology). It generalizes a well-known result of B. I. Dundas and R. McCarthy [ 2 ] established for the linear bifunctors.
The difference between these theories is computed in terms of homology of the category P ( R ) of finitely generated projectives with coefficients in certain bifunctors. And the final goal is achieved by proving the homology vanishing criterion for a very general class of bifunctors in the case of an arbitrary small additive category.
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