Quantum Sets of Compact Quantum Groups

Q-system completion can be thought of as a notion of higher idempotentcompletion of C*-2-categories. We introduce a notion of quantum bi-elements,and study Q-system completion in the context of compact quantum groups. Werelate our notion of quantum bi-elements to already known notions of quantumsets and quantum functions, and provide a description of Q-system completion ofthe C*-2-category of compact quantum groups using quantum bi-elements