  We provide a finite dimensional categorification of the symmetric evaluation
of $\mathfrak{sl}_N$-webs using foam technology. As an output we obtain a
symmetric link homology theory categorifying the link invariant associated to
symmetric powers of the standard representation of $\mathfrak{sl}_N$. In
addition, the construction is actually made in an equivariant setting. We prove
also that there is a spectral sequence from the Khovanov-Rozansky triply graded
link homology to the symmetric one and provide along the way a foam
interpretation of Soergel bimodules.
