The n-Category Café

Devotees of the $n$-Café will note that I gave a talk with a suspiciously similar title over a year ago. What’s new about this one?

Well, it’s not drastically different. But I’ve thought a lot more about 2-categories and the $\lambda$-calculus, so this goes into a bit more detail about that. And also there’s more of a focus on physics. Last year’s conference was on algebraic topology and computer science; now it’s logic and computer science — but I’ve been invited to talk about connections between these subjects and physics. So, I’m trying hard to explain how a 2-category of

• data types,
• terms, and
• rewrite rules

can resemble a 2-category of

• $D$-branes,
• states of a topological open string theory, and
• operators between open string states

and how this fits into the overall perspective of the ‘Periodic Table’ of $n$-categories. Doing this with any precision in one hour seems impossible, so I’m just trying to convey a rough flavor of the idea, while pointing people to a webpage for references that provide more details.

As with the previous incarnation of this talk, you understand it once you fully grok what these pictures mean: