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We categorify the Beilinson–Lusztig–MacPherson integral form of quantum sl ( 2 ) specialized at a prime root of unity. [ABSTRACT FROM AUTHOR]

We categorify an idempotented form of quantum sl 2 and some of its simple representations at a prime root of unity. [ABSTRACT FROM AUTHOR]

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 irreduciblemodules of the Temperley-Lieb algebra. [ABSTRACT FROM AUTHOR]