The category of non-crossing partitions with small blocks is a a Banica-Speicher category of partitions inducing the corepresentation category of the free bistochastic quantum groups.
By the category of non-crossing partitions with small blocks one denotes the subcategory of the category of all partitions whose morphism set is the set of all non-crossing partitions with small blocks. It was introduced by Banica and Speicher in [BanSp09].
The category of all non-crossing partitions with small blocks is the subcategory of generated by the partition .
Via Tannaka-Krein duality for compact quantum groups, the category of all non-crossing partitions with small blocks corresponds to the family of free bistochastic quantum groups.