The purpose of the present
paper is to develop some aspects of a cohomology theory in the category of C
comodules, where C is a bialgebra. This cohomology theory generalizes the
rational cohomology of affine algebraic groups and also the cohomology of Lie
Algebras. We develop the theory up to the point where we can guarantee the
convergence of the analogue of the Hochschild Serre spectral sequence and the
convergence of another spectral sequence, which is a natural generalization of
the result known as Shapiro’s lemma in the cohomology theory of finite
groups.
