Elias and Williamson gave a diagrammatic presentation by generators and relations of the Hecke category (one incarnation of which is, for instance, the category of Soergel bimodules). One can adapt this presentation to describe a dg version of the category of Rouquier complexes, which are defined in terms of the Hecke category and provide a categorification of the braid groups. I will describe the basic properties of this category and some results about Rouquier complexes that can be obtained from this point of view via Discrete Morse Theory techniques.