Abstract
Cofibrantly generated model categories are generalizations of CW-approximations which provide an inductive cofibrant replacement. We provide examples of inductive fibrant replacements constructed as Postnikov towers for simplicial and differential graded comodules. Our main application is to show that simplicial comodules and connective differential graded comodules are Quillen equivalent and their derived cotensor products correspond. We deduce that the rational A-theory of a simply connected space X is equivalent to the K-theory of perfect chain complexes with a C⁎(X;Q)-comodule structure.
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