Two-color Soergel calculus and simple transitive 2-representations
  In this paper we complete the $\mathrm{ADE}$-like classification of simple transitive $2$-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag algebras of $\mathrm{ADE}$ type to give an explicit construction of a graded (non-strict) version of all these $2$-representations.   Moreover, we give simple combinatorial criteria for when two such $2$-representations are equivalent and for when their Grothendieck groups give rise to isomorphic representations.   Finally, our construction also gives a large class of simple transitive $2$-representations in infinite dihedral type for general bipartite graphs. 
Marco Mackaay and Daniel Tubbenhauer
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