Titles and abstracts — junior seminar

Joan Bosa: Classification of monoids. Applications to the Cuntz semigroup. The Cuntz semigroup W (A), in its classical format, fails to be a continuous functor. This shortcoming was remedied by Coward, Elliott and Ivanescu who, in 2008, introduced a new category (called Cu) and a semigroup attached to any C∗-algebra A (called Cu(A)), which belongs to Cu. The assignment A 7→ Cu(A) is now continuous. It was also shown that Cu(A) can be identified with W (A⊗K). We define a new category, that we call PreCu, where W (A) naturally belongs. We show that there is a completion functor from PreCu to Cu, which is a left adjoint of the inclusion. With this construction, we obtain information about how W (A) and W (A⊗K) are related, and recover some known results.