  In this note we give explicit isomorphisms of 2-categories between various
versions of the categorified quantum group associated to a simply-laced
Kac-Moody algebra. These isomorphisms are convenient when working with the
categorified quantum group. They make it possible to translate results from the
gl(n) variant of the 2-category to the sl(n) variant and transfer results
between various conventions in the literature. We also extend isomorphisms of
finite type KLR algebras for different choices of parameters to the level of
2-categories.
