Monoidal 2-Categories
Monoidal 2-Categories
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.
Keywords: Monoidal 2-category, Categorification, Oriented duality, 2-Hilbert space, Deligne tensor product
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