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Within the framework of unitary easy quantum groups, we study an analogue ofBrauer's Schur-Weyl approach to the representation theory of the orthogonalgroup. We consider concrete combinatorial categories whose morphisms are formedby partitions of finite sets into disjoint subsets of cardinality two; thepoints of these sets are colored black or white. These categories correspond to"half-liberated easy" interpolations between the unitary group and Wang'squantum counterpart. We complete the classification of all such categoriesdemonstrating that the subcategories of a certain natural halfway point areequivalent to additive subsemigroups of the natural numbers; the categoriesabove this halfway point have been classified in a preceding article. Weachieve this using combinatorial means exclusively. Our work reveals that thehalf-liberation procedure is quite different from what was previously knownfrom the orthogonal case.

Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups