  In this note we present an explicit isomorphism between Khovanov-Rozansky
$sl_2$-homology and ordinary Khovanov homology. This result was originally
stated in Khovanov and Rozansky's paper \cite{KRI}, though the details have yet
to appear in the literature. The main missing detail is providing a coherent
choice of signs when identifying variables in the $sl_2$-homology. Along with
the behavior of the signs and local orientations in the $sl_2$-homology, both
theories behave differently when we try to extend their definitions to virtual
links, which seemed to suggest that the $sl_2$-homology may instead correspond
to a different variant of Khovanov homology. In this paper we describe both
theories and prove that they are in fact isomorphic by showing that a coherent
choice of signs can be made. In doing so we emphasize the interpretation of the
$sl_2$-complex as a cube of resolutions.
