The two-colored Temperley–Lieb algebra is a generalization of the Temperley–Lieb algebra. The analogous two-colored Jones–Wenzl projector plays an important role in the Elias–Williamson construction of the diagrammatic Hecke category. We give conditions for the existence and rotatability of 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.

中文翻译：

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双色琼斯-温茨尔投影仪的存在性和可旋转性

双色 Temperley-Lieb 代数是 Temperley-Lieb 代数的推广。类似的双色琼斯-温茨尔投影仪在埃利亚斯-威廉姆森图解赫克范畴的构建中发挥着重要作用。我们给出了存在和可旋转的条件就某些双色量子二项式系数的可逆性和消失而言。因此，我们证明了 Abe 的 Soergel 双模范畴在完全一般性上等价于图解 Hecke 范畴。