The category of partitions of even size is a Banica-Speicher category of partitions inducing the corepresentation category of the modified symmetric groups.
By the category of partitions of even size one denotes the subcategory of the category of all partitions whose morphism class is the set of all partitions of even size. It was introduced by Banica and Speicher in [BanSp09].
For all , a partition is said to be of even size if is an even number, i.e., if has evenly many points.
It is sometimes said that the category of partitions of even size is the even part of the category of all partitions.
The category of all 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 partitions of even size corresponds to the family of modified symmetric groups.