  We introduce three spectral sequences which give some expressions of colored
Jones polynomials. Each spectral sequence contains a Khovanov-type homology
groups. Two of them are derived from a bicomplex of the colored Jones
polynomial. The other is the spectral sequence that deduces a colored Rasmussen
invariant of links. We also introduce three functors between categories of
nanophrases, generalizations of links, and obtain their applications using
colored Jones polynomials and their categorifications.
