chalkdust
Highways Agency, CC BY 2.0
Aryan Ghobadi
A
s trends go, diagrammatic algebra has taken mathematics by storm. Appearing in papers on computer science, pure mathematics and theoretical physics, the concept has expanded well beyond its birthplace, the theory of Hopf algebras. Some use these diagrams to depict difficult processes in quantum mechanics; others use them to model grammar in the English language! In algebra, such diagrams provide a platform to prove difficult ring theoretic statements by simple pictures. As an algebraist, Iβd like to present you with a down-to-earth introduction to the world of diagrammatic algebra, by diagrammatising a rather simple structure: namely, the set of natural numbers! At the end, I will allude to the connections between these diagrams and the exciting world of higher and monoidal categories. Nowβimagine yourself in a lecture room, with many others as excited about diagrams as you (yes?!), plus a cranky audience member, who isnβt a fan of category theory, in the front row:
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