  The monoidal category of Soergel bimodules categorifies the Hecke algebra of
a finite Weyl group. In the case of the symmetric group, morphisms in this
category can be drawn as graphs in the plane. We define a quotient category,
also given in terms of planar graphs, which categorifies the Temperley-Lieb
algebra. Certain ideals appearing in this quotient are related both to the
1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We
demonstrate how further subquotients of this category will categorify the cell
modules of the Temperley-Lieb algebra.
