  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.
