  In this paper we categorify the q-Schur algebra S(n,d) as a quotient of
Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our
2-category contains Soergel's monoidal category of bimodules of type A, which
categorifies the Hecke algebra H(d), as a full sub-2-category if d does not
exceed n. For the latter result we use Elias and Khovanov's diagrammatic
presentation of Soergel's monoidal category of type A.
