  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$^*$-algebras $A$ and $B$, the semigroup $[[\mathrm{Cu}(A),\mathrm{Cu}(B)]]$
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 also show that order-zero maps between C$^*$-algebras naturally
define elements in the respective bivariant Cuntz semigroup.
