# 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}
}
• Published 6 February 2017
• Mathematics
• International Mathematics Research Notices
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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