A categorification of the integral form of the Cartan subalgebra for quantum sl(2)

We propose a categorification of the Lusztig integral form of the quantum Cartan subalgebra for $sl(2)$ via a colimit of categories of equivariant coherent sheaves on finite-dimensional projective spaces. The nonequivariant version of our construction yields a nonsemisimple abelian categorification of the ring of integer-valued polynomials.