Abstract Bivariant Cuntz Semigroups II

We previously showed that abstract Cuntz semigroups form a closed symmetric monoidal category. This automatically provides additional structure in the category, such as a composition and an external tensor product, for which we give concrete constructions in order to be used in applications. We further analyse the structure of not necessarily commutative Cu-semi-rings and we obtain, under mild conditions, a new characterization of solid Cu-semirings $R$ by the condition that $R\cong [\text{\hspace{0.17em}⁣}[R,R]\text{\hspace{0.17em}⁣}]$.