The diagrammatic Soergel category and sl(N)-foams, for N > 3

TL;DR

This paper constructs a monoidal functor linking Elias and Khovanov's diagrammatic Soergel category to sl(N) foams for N > 3, revealing how Soergel's category can be derived from these foams.

Contribution

It introduces a novel monoidal functor connecting the diagrammatic Soergel category with sl(N) foams for N > 3, providing a new perspective on their relationship.

Findings

Established a functor from Soergel's category to sl(N) foams

Demonstrated how Soergel's category can be obtained from sl(N) foams

Extended the framework to N > 3 cases

Abstract

For each N > 3, 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, Stosic and Vaz. We show that through these functors Soergel's category can be obtained from the sl(N) foams.