John Baez, one of the organizers of the workshop, is also going through them and adding some interesting background and links on his Azimuth blog as well for those who are looking for additional details and depth.

]]>There is one more blog to mention: John Baez has recently been writing about PROPs and linear systems; check it out if you want a sneak preview of one of the star applications of graphical linear algebra! John and his student Jason Erbele developed the theory independently and more or less at the same time as Filippo, Fabio and I. But, apart from the fact that they have different conventions for drawing diagrams, the equational theory that they have developed can be shown to be equivalent to the one we will develop here. It’s super interesting that science is full of temporal coincidences like this; it’s not even the first time that this kind of thing happens to me!

]]>If our field is the good old real numbers, we write as an abbreviation for The direct sum of objects is

which we abbreviate as addition of natural numbers: adding and gives We write

to mean a linear map

or more concretely an matrix. We compose these maps by matrix multiplication. And given linear maps

and

we get a linear map

corresponding to the block diagonal matrix with and as its blocks.

All this stuff is called the PROP Then you can replace by any other commutative rig.

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