  We discuss a new perspective on Khovanov homology, using categorifications of
tensor products. While in many ways more technically demanding than Khovanov's
approach (and its extension by Bar-Natan), this has distinct advantage of
directly connecting Khovanov homology to a categorification of
\$(\mathbb{C}^2)^{\otimes \ell}\$, and admitting a direct generalization to
other Lie algebras.
  While the construction discussed is a special case of that given in previous
work of the author, this paper contains new results about the special case of
\$\mathfrak{sl}_2\$ showing an explicit connection to Bar-Natan's approach to
Khovanov homology, to the geometry of Grassmannians, and to the categorified
Jones-Wenzl projectors of Cooper and Krushkal. In particular, we show that the
colored Jones homology defined by our approach coincides with that of Cooper
and Krushkal.
