  The two-colored Temperley-Lieb algebra $2\mathrm{TL}_R({}_s {n})$ is a
generalization of the Temperley-Lieb algebra. The analogous two-colored
Jones-Wenzl projector $\mathrm{JW}_R({}_s {n}) \in 2\mathrm{TL}_R({}_s {n})$
plays an important role in the Elias-Williamson construction of the
diagrammatic Hecke category. We give conditions for the existence and
rotatability of $\mathrm{JW}_R({}_s {n})$ in terms of the invertibility and
vanishing of certain two-colored quantum binomial coefficients. As a
consequence, we prove that Abe's category of Soergel bimodules is equivalent to
the diagrammatic Hecke category in complete generality.
