The stable uniqueness theorem for unitary tensor category equivariant KK-theory

Abstract

We introduce the Cuntz-Thomsen picture of $\mathcal{C}$-equivariant Kasparov theory, denoted ${\mathrm{KK}}^{\mathcal{C}}$, for a unitary tensor category $\mathcal{C}$ with countably many isomorphism classes of simple objects. We use this description of ${\mathrm{KK}}^{\mathcal{C}}$ to prove the stable uniqueness theorem in this setting.

References in corpus (6)

• Quasidiagonality of nuclear C*-algebras
• Equivariant Kasparov theory and generalized homomorphisms
• Strongly self-absorbing C*-dynamical systems, III
• Q-system completion for C* 2-categories
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras
• Tensor category equivariant KK-theory