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

TL;DR

This paper develops a new framework for equivariant KK-theory using the Cuntz-Thomsen picture for unitary tensor categories and proves a stable uniqueness theorem within this setting.

Contribution

It introduces the Cuntz-Thomsen model for $ ext{KK}^ ext{C}$ and establishes the stable uniqueness theorem for this class of categories.

Findings

Defined the Cuntz-Thomsen picture for $ ext{KK}^ ext{C}$.

Proved the stable uniqueness theorem for $ ext{KK}^ ext{C}$.

Enhanced understanding of equivariant KK-theory for tensor categories.

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.