Injectivity for algebras and categories with quantum symmetry

Key Points

• The aim is to demonstrate the existence of injective envelopes for certain quantum algebras and categories.
• Established existence of injective envelopes for unital Yetter–Drinfeld C∗-algebras.
• Analyzed bimodule categories over rigid C∗-tensor categories.
• Investigated boundary actions of Drinfeld doubles of compact quantum groups.
• Confirmed the existence of injective envelopes in the studied algebras and categories.
• Proved that this existence implies monoidal invariance of boundary actions.
• Demonstrated how these results relate to quantum symmetry in algebraic structures.