====== Brauer category ======

**Brauer category** also known as the **category of all pairings** is a diagrammatical category, where the objects are formed by sets of points (equivalently natural numbers) and morphisms are pairings of the points formed by the domain and codomain. It can be understood as a subcategory of the [[category_of_all_partitions|category of all partitions]] if we consider only those partitions that have all blocks of size two -- //pair partitions// or //pairings//. As an important subcategory it contains the [[Temperley–Lieb Category|Temperley–Lieb Category]]. It models the representation theory of the orthogonal group $O_N$.