Injectivity for algebras and categories with quantum symmetry

Abstract

We establish the existence of injective envelopes for unital Yetter-Drinfeld C*-algebras, and a related class of bimodule categories over rigid C*-tensor categories. This implies monoidal invariance for boundary actions of Drinfeld doubles of compact quantum groups.

v3: 24 pages, duality part is split off as arXiv:2504.21162; v2: 34 pages, minor changes; v1: 31 pages