Nice pictures, Michael!

Keith is right: associativity should go from \\((x \otimes y) \otimes z\\) to \\(x \otimes (y \otimes z)\\) and also back the other way... but a nice feature of wiring diagrams it that _we can leave associativity implicit!_ Since there are no parentheses in the wiring diagrams, we can write \\(x\\), \\(y\\) and \\(z\\) as parallel wires next to each other without \\(\otimes\\) symbols, and this stands for both \\((x \otimes y) \otimes z\\) and \\(x \otimes (y \otimes z)\\).

Another smaller issue: "communitivity" should be "commutativity".

There are probably some other ways to polish and perfect these pictures, but I'll let other people have fun figuring out the very best ways to draw them.

Keith is right: associativity should go from \\((x \otimes y) \otimes z\\) to \\(x \otimes (y \otimes z)\\) and also back the other way... but a nice feature of wiring diagrams it that _we can leave associativity implicit!_ Since there are no parentheses in the wiring diagrams, we can write \\(x\\), \\(y\\) and \\(z\\) as parallel wires next to each other without \\(\otimes\\) symbols, and this stands for both \\((x \otimes y) \otimes z\\) and \\(x \otimes (y \otimes z)\\).

Another smaller issue: "communitivity" should be "commutativity".

There are probably some other ways to polish and perfect these pictures, but I'll let other people have fun figuring out the very best ways to draw them.