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arXiv · 2409.17465

Exactness of the Cuntz-Pimsner Construction

Menevşe Eryüzlü Paulovicks
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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.

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Menevşe Eryüzlü Paulovicks. 2024-09-26. Exactness of the Cuntz-Pimsner Construction. https://arxiv.org/abs/2409.17465

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