  For differential calculi on noncommutative algebras, we construct a twisted
de Rham cohomology using flat connections on modules. This has properties
similar, in some respects, to sheaf cohomology on topological spaces. We also
discuss generalised mapping properties of these theories, and relations of
these properties to corings. Using this, we give conditions for the Serre
spectral sequence to hold for a noncommutative fibration. This might be better
read as giving the definition of a fibration in noncommutative differential
geometry. We also study the multiplicative structure of such spectral
sequences. Finally we show that some noncommutative homogeneous spaces satisfy
the conditions to be such a fibration, and in the process clarify the
differential structure on these homogeneous spaces. We also give two explicit
examples of differential fibrations: these are built on the quantum Hopf
fibration with two different differential structures.
