Partition categories also known as linear categories of partitions have been recently heavily studied by researchers from different fields of mathematics and physics such as group theory, compact quantum groups, operator algebras, tensor categories or statistical physics. In the theory of (compact quantum) groups they are used to model the representation theory of a given quantum group.

Note that in the theory of compact matrix quantum groups, the term category of partitions often means an easy category of partitions in the sense of Banica and Speicher.

A linear category of partitions is a rigid monoidal -subcategory of the linear category of all partitions.

• Category of partitions
• Tannaka--Krein duality