On Strict Higher C*-categories
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.
Keywords
Cite
@article{arxiv.1709.09339,
title = {On Strict Higher C*-categories},
author = {Paolo Bertozzini and Roberto Conti and Wicharn Lewkeeratiyutkul and Noppakhun Suthichitranont},
journal= {arXiv preprint arXiv:1709.09339},
year = {2025}
}
Comments
57 pages, AMS-LaTeX2e, very expanded introduction, several typos corrected, results unchanged; this is a reformatted version (only for arXiv) of the published paper, with two additional clarifying notes (in footnote 48 and 57)