The category of non-crossing two-colored pair partitions with neutral blocks is a category of two-colored partitions inducing the co-representation categories of the free unitary quantum group.
By the category of non-crossing two-colored pair partitions with neutral blocks one denotes the subcategory of the category of all two-colored partitions whose morphism class is the set of all non-crossing pair partitions with neutral blocks. It was introduced by Tarrago and Weber in [TaWe18], Proposition 3.3 (a) under the name .
The set of non-crossing two-colored pair partitions with neutral blocks is the morphism set of the subcategory of generated by the empty set of two-colored partitions. It is the minimal category of two-colored partitions.
The category of non-crossing two-colored pair partitions with neutral blocks induces the co-representation categories of the free unitary quantum groups , defined by Wang in [Wang95], Example 4.2.