Frenkel gives an introductory lecture on the link between the Langlands program and physics.
Frenkel: The most important thing about branes is that they are objects in a category ... it really comes down to an equivalence of categories of branes.
Audience: What is a category?
Frenkel: Er ...
Frenkel: The big question then, is where does the S duality come from? There is a mysterious six dimensional theory, that I would like to talk about, but the blackboard is too small to contain it ...
14 years ago
Those who are following will realise that we are talking about six categorical dimensions. Braids in three dimensions are thickened to surfaces using duality. Whereas symmetric monoidal categories have two empty levels (one for $\otimes$ and one for a braiding), a nice $6$-category will have three empty levels, or products.
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