  We consider colored operads and their actions on categories. As a special
example we construct a cobordism category with a colored operad action arising
from oriented planar arc diagrams. This is used to construct an invariant of
oriented tangle diagrams with values in the homotopy category attached to the
cobordism category. Motivated by Bar-Natan's categorification of the Jones
polynomial, it categorifies the quantum $sl_n$ quantum invariants and is
adapted to the categorification of the $sl_n$ quantum invariants by Khovanov
and Rozansky using matrix factorizations. We conjecture to exist the
consistency of the cobordism category and to have an explicit functor from the
cobordism category to a category of matrix factorizations.
