Bivariant cyclic cohomology and models for cyclic homology types (Q1898413)

The notions of a mixed complex and of an \(S\)-module of vector spaces over \(\mathbb{C}\) -- both are chain complexes equipped with a certain operator -- give a wide-ranging description of cyclic homology types. Using results of \textit{C. Kassel} [Cyclic homology, comodules, and mixed complexes, J. Algebra 107, 195-216 (1987; Zbl 0617.16015)] the following categories are proved to be 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.