2024/04/08 by Giovanni Ferrer, Ferrer, Giovanni
Computer Science · Mathematics · #46M15 18N20 18M40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2404.05193
openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An operator algebraic tricategory is a higher categorical analogue of an operator algebra. For algebraic tricategories, Gordon, Power, and Street proved that every algebraic tricategory is equivalent to a Gray-category, a result later refined by Gurski. We adapt this result to the context of functional analysis, showing that every operator algebraic tricategory is equivalent to an operator Gray-category. We then categorify the Gelfand-Naimark theorem for operator algebras, inductively proving that every (small) operator algebraic tricategory is equivalent to a concrete operator Gray-category. We also provide several examples of interest for operator algebraic tricategories.