  In this paper, which is a follow-up to my paper with Yonezawa "sl(N)-web
categories", I define and study sl(N)-web algebras for any N greater than one.
For N=2 these algebras are isomorphic to Khovanov's arc algebras and for N=3
they are Morita equivalent to the sl(3)-web algebras which I defined and
studied with Pan and Tubbenhauer.
  The main result of this paper is that the sl(N)-web algebras are Morita
equivalent to blocks of certain level-N cyclotomic KLR algebras, for which I
use the categorified quantum skew Howe duality from the aforementioned paper
with Yonezawa.
  Using this Morita equivalence and Brundan and Kleshchev's work on cyclotomic
KLR algebras, I show that there exists an isomorphism between a certain space
of sl(N)-webs and the split Grothendieck group of the corresponding sl(N)-web
algebra, which maps the dual canonical basis elements to the Grothendieck
classes of the indecomposable projective modules (with a certain normalization
of their grading).
