$C^*$-correspondence functoriality of Cuntz-Pimsner algebras

M. Eryüzlü

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arXiv · 2009.08488

$C^*$-correspondence functoriality of Cuntz-Pimsner algebras

M. Eryüzlü

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Abstract

We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner algebras. The objects in our domain category are $C^*$-correspondences, and the morphisms are the isomorphism classes of $C^*$-correspondences satisfying certain conditions. As an application, we recover a well-known result of Muhly and Solel. In fact, we show that functoriality leads us to a more generalized result: strongly Morita equivalent $C^*$-correspondences have Morita equivalent Cuntz-Pimsner algebras.

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BibTeX RIS

M. Eryüzlü. 2020-09-17. $C^*$-correspondence functoriality of Cuntz-Pimsner algebras. https://arxiv.org/abs/2009.08488

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