Functoriality of Cuntz-Pimsner correspondence maps

Abstract

We show that the passage from a $C^{\ast }$-correspondence to its Cuntz-Pimsner $C^{\ast }$-algebra gives a functor on a category of $C^{\ast }$-correspondences with appropriately defined morphisms. Applications involving topological graph $C^{\ast }$-algebras are discussed, and an application to crossed-product correspondences is presented in detail.

16 pages

Cited by in corpus (2)

• Coactions on Cuntz-Pimsner algebras
• Coactions and skew products for topological graphs