### The Catsters Strike Again: “String Diagrams”

#### Posted by John Baez

You may have thought the Catsters was a funny stage name for Eugenia Cheng… but now the other Catster,

Simon Willerton, steps in front of the camera and demonstrates

*his* star power:

This guy is full of energy. Watch how he literally

*bursts* onstage at the beginning of the second act!

Category theory is great stuff, but it can easily seem ‘too abstract’ before you see how much of it can be done by wiggling around pieces of string! I tried to explain this back in the early days of the Quantum Gravity Seminar — in track 1 of the

Fall 2000 and

Winter 2001 notes. But, for explaining how to do math with pictures, videos are better.

Posted at September 24, 2007 9:29 PM UTC
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## Re: The Catsters Strike Again: “String Diagrams”

You know, it sometimes bothers me when people complain that category theory is too abstract – to me the modes of reasoning seem no more or less abstract than a lot of what goes on in algebra. But perhaps it’s the

perceivedlack of geometric “hooks” that explains people’s discomfort – the sort of thing that makes string diagrams come as such a relief.The yanking moves associated with triangular identities of an adjunction are just the tip of an iceberg: they are the lowest-dimensional examples of cancellation of critical points in Morse theory. Interchange equalities give rearrangements of such critical points. There is a general yoga of cancellation and rearrangement of critical points in Morse theory (used in proofs of the h-cobordism theorem, among other things), and it seems to me it would be desirable to give a full n-categorical account of this yoga. Surely this sort of thing has been considered by many people, but has there been serious work on this? (There’s been some work in low dimensions, and surely this sort of thing is implicit in the cobordism conjecture, but I don’t know of much beyond that.)