Joint with M. Khovanov

We develop a diagrammatic categorification of the polynomial ring Z[x], based on the geometrically defined graded algebra and show how to lift various operations on polynomials to the categorified setting. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to xn and standard modules to (x-1)n in the Grothendieck ring. This construction is generalized to the categorizcation of some basic special functions, such as Chebyshev polynomials.