  We provide examples of inductive fibrant replacements in fibrantly generated
model categories constructed as Postnikov towers. These provide new types of
arguments to compute homotopy limits in model categories. We provide examples
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 $C_*(X; \mathbb{Q})$-comodule
structure.
