  We define a quotient of the category of finitely generated modules over the
cyclotomic Khovanov-Lauda-Rouquier algebra for type An and show it has a module
category structure over a direct sum of certain cyclotomic
Khovanov-Lauda-Rouquier algebras of type An-1, this way categorifying the
branching rules for the inclusion of sl(n) in sl(n+1). Using this we give a
new, elementary proof of Khovanov-Lauda cyclotomic conjecture. We show that
continuing recursively gives the Gelfand-Tsetlin basis for type An. As an
application we prove a conjecture of Mackaay, Stosic and Vaz concerning
categorical Weyl modules.
