The category of non-crossing partitions of even size is a Banica-Speicher category of partitions inducing the corepresentation category of the free modified symmetric quantum groups.
By the category of non-crossing partitions of even size one denotes the subcategory of the category of all partitions whose morphism class is the set of all non-crossing partitions of even size. It was introduced by Banica and Speicher in [BanSp09].
It is sometimes said that the category of non-crossing partitions of even size is the even part of the category of all non-crossing partitions.
The category of all non-crossing partitions of even size is the subcategory of generated by the set of partitions .
Via Tannaka-Krein duality for compact quantum groups, the category of all non-crossing partitions of even size corresponds to the family of free modified symmetric quantum groups.