International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 468968, 20 pages
Research Article

The Diagrammatic Soergel Category and sl(N)-Foams, for N4

1Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
2CAMGSD, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
3Institut de Mathématiques de Jussieu, Université Paris 7, 175 Rue du Chevaleret, 75013 Paris, France

Received 17 November 2009; Accepted 10 April 2010

Academic Editor: Aaron Lauda

Copyright © 2010 Marco Mackaay and Pedro Vaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For each N4, we define a monoidal functor from Elias and Khovanov's diagrammatic version of Soergel's category of bimodules to the category of sl(N) foams defined by Mackaay, Stošić, and Vaz. We show that through these functors Soergel's category can be obtained from the sl(N) foams.