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Category of partitions with small blocks
The category of partitions with small blocks is a Banica-Speicher category of partitions inducing the corepresentation category of the bistochastic groups.
Definition
By the category of partitions with small blocks one denotes the subcategory of the category of all partitions 
whose underlying set is the set of all partitions with small blocks.
A partition 
is said to have small blocks if every block in 
is of size 
or 
.
The set of all pair partitions with small blocks is denoted by 
in [BanSp09].
Canonical generator
The category of partitions 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 with small blocks corresponds to the family 
of bistochastic groups.
References
