Geodesic
A Categorification of One-Variable Polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015).

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We develop a diagrammatic categorification of the polynomial ring $\mathbb{Z} [x]$, based on a geometrically-defined graded algebra and show how to lift various operations on polynomials to the categorified setting. Our categorification satisfies a version of the Bernstein-Gelfand-Gelfand reciprocity property, with indecomposable projective modules corresponding to $x^n$ and standard modules to $(x -1)^n$ in the Grothendieck ring. This construction generalizes tocategorification of various orthogonal polynomials. 
@article{DMTCS_2015_special_285_a12,
     author = {Khovanov, Mikhail and Sazdanovic, Radmila},
     title = {A {Categorification} of {One-Variable} {Polynomials}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)},
     year = {2015},
     doi = {10.46298/dmtcs.2468},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2468/}
}
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%A Sazdanovic, Radmila
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%D 2015
%V DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
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Khovanov, Mikhail; Sazdanovic, Radmila. A Categorification of One-Variable Polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) (2015). doi : 10.46298/dmtcs.2468. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2468/

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