ct.category theory – Relation Hopf Categories and Categorified Quantum Groups

In the paper Hopf Categories Crane and Frenkel gave a definition of a Hopf category, which they considered as a categorification of a quantum group. Categorifications of quantum groups have later been defined by Rouquier in 2-Kac-Moody groups and Khovanov and Lauda in their series of papers KL1, KL2 and KL3. The latter is in fact a 2-category not a category, where the former seems to be representation categories of something called trialgebras.

Are there any results on the relation of the two notions of categorification of quantum groups?