2024/09/26 by Paulovicks, Menevşe Eryüzlü
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2409.17465
In prior work we described how the Cuntz-Pimsner construction may be viewed as a functor. The domain of this functor is a category whose objects are C^*-correspondences and morphisms are isomorphism classes of certain pairs comprised of a C^*-correspondence and an isomorphism. The codomain is the well-studied category whose objects are C^*-algebras and morphisms are isomorphism classes of C^*-correspondences. In this paper we show that certain fundamental results in the theory of Cuntz-Pimsner algebras are direct consequences of the functoriality of the Cuntz-Pimsner construction. In addition, we describe exact sequences in the target and domain categories, and prove that the Cuntz-Pimsner functor is exact.