This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Antoine, RamonPerera, FrancescThiel, Hannes2019-06-2820171864-7596https://doi.org/10.34657/1929https://oa.tib.eu/renate/handle/123456789/2377We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups S and T, there is another Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as the target in analogues of the UCT for bivariant theories of Cuntz semigroups. Abstract bivariant Cuntz semigroups are computable in a number of interesting cases. We explore its behaviour under the tensor product with the Cuntz semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra. We also show that order-zero maps between C*-algebras naturally define elements in the respective bivariant Cuntz semigroup.application/pdfeng510Cuntz semigrouptensor productcontinuous posetC*-algebraReport