The category of partitions of even size with small blocks and even distances between legs is a Banica-Speicher category of partitions inducing the corepresentation category of the half-liberated bistochastic quantum groups.
By the category of partitions of even size with small blocks and even distances between legs one denotes the subcategory of the category of all partitions whose morphism class is the set of partitions of even size with small blocks and even distances between legs. It was introduced by Weber in [Web12].
A partition belongs to this set if the following conditions are met:
In particular, the category of partitions of even size with small blocks and even distances between legs is a subcategory of the categories of partitions of even size and of partitions with small blocks.
The category of partitions of even size with small blocks and even distances between legs is the subcategory of generated by the partitions . The partition embodies the half-commutation relations .
Via Tannaka-Krein duality for compact quantum groups, the category of partitions of even size with small blocks and even distances between legs corresponds to the family of half-liberated bistochastic quantum groups.