  We want to construct a homological link invariant whose Euler characteristic
is MOY polynomial as Khovanov and Rozansky constructed a categorification of
HOMFLY polynomial. The present paper gives the first step to construct a
categorification of MOY polynomial. For the essential colored planar diagrams
with additional data which is a sequence naturally induced by coloring, we
define matrix factorizations, and then we define a matrix factorization for
planar diagram obtained by gluing the essential colored planar diagrams as
tensor product of the matrix factorizations for the essential planar diagrams.
Moreover, we show that some matrix factorizations deribed from tensor product
of the essential matrix factorizations have homotopy equivalences corresponding
to MOY relations.
