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arXiv · 1709.09339

On Strict Higher C*-categories

Paolo Bertozzini·Roberto Conti·Wicharn Lewkeeratiyutkul·Noppakhun Suthichitranont
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Abstract

We provide definitions for strict involutive higher categories (a vertical categorification of dagger categories), strict higher C*-categories and higher Fell bundles (over arbitrary involutive higher topological categories). We put forward a proposal for a relaxed form of the exchange property for higher (C*)-categories that avoids the Eckmann-Hilton collapse and hence allows the construction of explicit non-trivial "non-commutative" examples arising from the study of hypermatrices and hyper-C*-algebras, here defined. Alternatives to the usual globular and cubical settings for strict higher categories are also explored. Applications of these non-commutative higher C*-categories are envisaged in the study of morphisms in non-commutative geometry and in the algebraic formulation of relational quantum theory.

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Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul, Noppakhun Suthichitranont. 2017-09-27. On Strict Higher C*-categories. https://arxiv.org/abs/1709.09339

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