Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Ferrer, Giovanni
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4394673048