If I had to sum up what string diagrams are about in just a few words, I'd say "doing algebra with geometry". Sadly the term "geometric algebra" already got used up for something else. (I have no idea what geometric algebra is, even after scrolling through its wikipedia article)
Well, I wouldn't say it's all that tricky, myself. I guess it mostly just comes down to how experienced you are with tensor-algebraic manipulations. To an ascended master of Penrosian abstract indices and their myriad uses, it's actually pretty straightforward.
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I can handle it in my sleep, but I wanted to hint that this map - from the Clifford algebra, which is a filtered algebra, to its "associated graded algebra", the exterior algebra - is an isomorphism of vector spaces but not algebras. 1/2
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Without bearing this in mind one might think "xy and yx have degree 2, so they correspond to bivectors, while xy+yx =2<x,y>I has degree 0, so it corresponds to a scalar - contradiction!" In fact this relation means the Clifford algebra isn't Z-graded - just Z/2-graded.
End of conversation
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