Abstract bivariant Cuntz semigroups II

Ramon Antoine; Francesc Perera; Hannes Thiel

doi:10.1515/forum-2018-0285

Abstract bivariant Cuntz semigroups II

Ramon Antoine, Francesc Perera, Hannes Thiel

Department of Mathematics

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Abstract

©2019 Walter de Gruyter GmbH, Berlin/Boston. We previously showed that abstract Cuntz semigroups form a closed symmetric monoidal category. This automatically provides additional structure in the category, such as a composition and an external tensor product, for which we give concrete constructions in order to be used in applications. We further analyze the structure of not necessarily commutative Cu -semirings, and we obtain, under mild conditions, a new characterization of solid Cu -semirings R by the condition that R ≅ R, R.

Original language	English
Journal	Forum Mathematicum
DOIs	https://doi.org/10.1515/forum-2018-0285
Publication status	Published - 1 Jan 2019

Keywords

continuous poset
Cuntz semigroup
tensor product

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N2 - ©2019 Walter de Gruyter GmbH, Berlin/Boston. We previously showed that abstract Cuntz semigroups form a closed symmetric monoidal category. This automatically provides additional structure in the category, such as a composition and an external tensor product, for which we give concrete constructions in order to be used in applications. We further analyze the structure of not necessarily commutative Cu -semirings, and we obtain, under mild conditions, a new characterization of solid Cu -semirings R by the condition that R ≅ R, R.

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KW - continuous poset

KW - Cuntz semigroup

KW - tensor product

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