Bivariant cyclic cohomology and models for cyclic homology types Original Research Article

This paper concerns types of algebraic objects, such as mixed complexes and S-modules, which are used to obtain the homology and cohomology of interest in cyclic homology theory. We prove that the following five categories are equivalent: The derived category of mixed complexes. The homotopy category of free mixed complexes. The derived category of S-modules. The homotopy category of divisible S-modules. The homotopy category of special towers of supercomplexes. Thus any of these categories represents the category of cyclic homotopy types.