Completions of monoids with applications to the Cuntz semigroup

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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.
Original languageEnglish
Pages (from-to)837-861
JournalInternational Journal of Mathematics
Publication statusPublished - 1 Jun 2011


  • Completions
  • Cuntz semigroup
  • Elliott invariant
  • classification


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