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New York Journal of Mathematics
Volume 32 (2026), 748-767

  

Menevse Eryuzlu Paulovicks

Exactness of the Cuntz-Pimsner construction

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Published: May 9, 2026.
Keywords: C*-correspondence, Cuntz-Pimsner algebra, exact sequence, exact functor.
Subject [2020]: Primary 46L08; Secondary 18B99.

Abstract
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.

Acknowledgements

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Author information

Menevse Eryuzlu Paulovicks
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003-8001, USA

menevse.paulovicks@gmail.com