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We develop a diagrammatic categorification of the polynomial ring Z[x], basedon a geometrically defined graded algebra. This construction generalizes tocategorification of some special functions, such as Chebyshev polynomials.Diagrammatic algebras featured in these categorifications lead to the firsttopological interpretations of the Bernstein-Gelfand-Gelfand reciprocityproperty.

Diagrammatic categorification of the Chebyshev polynomials of the second kind