Categories of two-colored pair partitions Part II: Categories indexed by semigroups

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