  We prove that the category of abstract Cuntz semigroups is bicomplete. As a
consequence, the category admits products and ultraproducts. We further show
that the scaled Cuntz semigroup of the (ultra)product of a family of
C*-algebras agrees with the (ultra)product of the scaled Cuntz semigroups of
the involved C*-algebras.
  As applications of our results, we compute the non-stable K-Theory of general
(ultra)products of C*-algebras and we characterize when ultraproducts are
simple. We also give criteria that determine order properties of these objects,
such as almost unperforation.
