Abstract Bivariant Cuntz Semigroups

@article{Antoine2018AbstractBC,
  title={Abstract Bivariant Cuntz Semigroups},
  author={Ramon Antoine and Francesc Perera and Hannes Thiel},
  journal={International Mathematics Research Notices},
  year={2018}
}
We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups $S$ and $T$, there is another Cuntz semigroup $[\![ S,T ]\!] $ playing the role of morphisms from $S$ to $T$. Applied to $C^{\ast }$-algebras $A$ and $B$, the semigroup $[\![ \operatorname{Cu}(A),\operatorname{Cu}(B) ]\!] $ should be considered as the target in analogs of the universal coefficient theorem for bivariant theories of Cuntz semigroups. Abstract bivariant Cuntz semigroups… 

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