Proofs in braided monoidal categories using strings

Braided monoidal structures occur on categories whose objects are representations of (quantum) groups and on categories whose morphisms are low-dimensional manifolds. My purpose is to explain the use of string diagrams in these categories, motivated by linear algebra. As an application I shall use a string argument, influenced strongly by the work of Markus Rost and his students, to reprove the existence of very few dimensions on which division algebra structures can exist.