In a joint work with Marco Mackaay, we categorify the extended affine type A Hecke algebra and the affine quantum Schur algebra S(n,r) for 2 < r < n, using Elias-Khovanov and Khovanov-Lauda type diagrams. We also define an extension of the 2-categories of affine (singular) Soergel bimodules and construct the affine analogue of the Elias-Khovanov and the Khovanov-Lauda 2-representations of our diagrammatic categorifications into these bimodules 2-categories.

In this talk, the aim is to present categorification and in particular its diagrammatic approach, which has the benefit of working with more handable categories but also provides descriptions by generators and relations of abstract categories. We will illustrate this in detail by describing both the extended affine Soergel category and its diagrammatic counterpart, which categorify the extended Hecke algebra of affine type A. If time permits, we will treat the case of the affine Schur algebra.