Functoriality of Cuntz-Pimsner correspondence maps
  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. 
S. Kaliszewski, John Quigg and David Robertson
math.OA