MSGSS
The Eckmann-Hilton argument
This talk will be about one of my favorite facts, that if a set has two compatible multiplication maps then these operations agree, and it is commutative, and it’s one (or three) line proof. By moving from sets to categories the (proof of the) Eckmann-Hilton argument becomes the mere structure of a braiding in the category. If the category has three multiplications maps instead, then it does acquire the property of being commutative. This story has a nice pictorial interpretation in terms of the topology of embedded points and strings, and the real goal of the talk is to explore these ideas in terms of this more palatable point of view.