We provide an abstract categorical framework that relates the Cuntz semigroups of the C*-algebras A and A ⊗ K. This is done through a certain completion of ordered monoids by adding suprema of countable ascending sequences. Our construction is rather explicit and we show it is functorial and unique up to isomorphism. This approach is used in some applications to compute the stabilized Cuntz semigroup of certain C*-algebras. © 2011 World Scientific Publishing Company.
- Cuntz semigroup
- Elliott invariant