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Category of partitions with blocks of even size
The category of partitions with blocks of even size is a Banica-Speicher category of partitions inducing the corepresentation category of the hyperoctahedral groups.
Definition
By the category of partitions with blocks of even size one denotes the subcategory of the category of all partitions 
whose morphism set is the set of all partitions with blocks of even size. It was introduced by Banica, Bichon and Collins in [BanBichColl07].
This name is to be taken literally. A partition 
is said to have blocks of even size if every block of 
has an even number of legs.
Canonical generator
The category of partitions with blocks of even size is the subcategory of generated by the set 
of partitions.
Associated easy quantum groups
Via Tannaka-Krein duality for compact quantum groups, the category of all partitions with blocks of even size corresponds to the family 
of hyperoctahedral groups.
References
