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Category of two-colored partitions
Categories of two-colored partitions are certain strict monoidal involutive categories, introduced by Freslon and Weber in [FreWeb16], Definition 6.1. Each such category induces the co-representation categories of a sequence of unitary easy quantum groups. Categories of two-colored partitions generalize categories of (uncolored) partitions as defined by Banica and Speicher in [BanSp09].
Definition
The original definition of Freslon and Weber in [FreWeb16], Definition 6.1 was later equivalently reformulated by Tarrago and Weber in [TaWe18], Section 1.3. In this formulation, a category of two-colored partitions is a subset 
of the set 
of all two-colored partitions satisfying the following conditions with respect to the operations for two-colored partitions:
.
for all 
such that 
is composable.
for all 
.
for every 
.
References
