Temperley–Lieb category

Temperley–Lieb category also known as the category of all non-crossing pairings is a subcategory of the Brauer category, where we consider only non-crossing pairings. It is the smallest possible Linear category of partitions. It models the representation theory of the free orthogonal group $O_N^+$, more generally also the universal orthogonal groups $O_F^+$ and also the quantum special linear groups $SL_q(2)$.