Monoidal 2-categories are higher-dimensional versions of monoidal categories, allowing a more expressive syntax that plays an important role in modern mathematics. We explore their two-dimensional graphical calculus, and show how duality gives a language for oriented surfaces, from which Frobenius algebras emerge in a natural way. We describe 2-Hilbert spaces, categorifications of Hilbert spaces and explore the monoidal 2-category 2Hilb that they give rise to. We then show how we can use dualities in 2Hilb to give a concise and purely topological language to reason about teleportation, dense coding and complementarity.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.