In this paper, we consider "diagrams of rings", or functors from a small category to the category of rings, and the corresponding diagrams of groups Ki. Classically, this was initiated by Milnor. The main result of this paper is the direct comparison of the filtration in classical algebraic K-theory discussed in [6, 7] to a corresponding filtration in the Bousfield-Kan spectral sequence associated to a Tot-tower of simplicial groups attached to the diagram of rings.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.13-58.