====== Temperley–Lieb category ======

**Temperley–Lieb category** also known as the **category of all non-crossing pairings** is a subcategory of the [[brauer_category|Brauer category]], where we consider only non-crossing pairings. It is the smallest possible [[linear_category_of_partitions|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 $SL_q(2)$.