Categorification of the polynomial ring

Abstract

We develop a diagrammatic categorification of the polynomial ring $Z[x]$. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to $x^n$ and standard modules to $(x-1{)}^n$ in the Grothendieck ring.

29 pages, 26 figures