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Category of partitions of even size with small blocks
The category of partitions of even size with small blocks is a Banica-Speicher category of partitions inducing the corepresentation category of the modified bistochastic groups.
Definition
By the category of partitions of even size with small blocks one denotes the subcategory of the category of all partitions 
whose underlying set is the set of all partitions of even size with small blocks. It was introduced by Banica and Speicher in [BanSp09].
This name is to be taken literally.
- For all
, a partition 
is said to be of even size if 
is an even number, i.e., if 
has evenly many points. - And is said to have small blocks if every block in is of size
or 
.
In particular, the set of all partitions of even size with small blocks is the intersection of the morphism sets of two larger categories, the category of partitions of even size and the category of all partitions with small blocks.
Canonical generator
The category of partitions of even size with small blocks 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 of even size with small blocks corresponds to the family 
of modified bistochastic groups.
References
