Functoriality of Cuntz-Pimsner correspondence maps

TL;DR

This paper demonstrates that the process of associating a Cuntz-Pimsner algebra to a $C^*$-correspondence is functorial, with applications to topological graph algebras and crossed-product correspondences.

Contribution

It establishes the functorial nature of the Cuntz-Pimsner construction within a category of $C^*$-correspondences, extending the theoretical framework.

Findings

Functoriality of the Cuntz-Pimsner algebra construction

Applications to topological graph $C^*$-algebras

Detailed analysis of crossed-product correspondences

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.