Added

- Dan Ghica, Fabio Zanasi,
*Hierarchical string diagrams and applications*(arXiv:2305.18945)

Added

- Robin Piedeleu, Fabio Zanasi,
*An Introduction to String Diagrams for Computer Scientists*(arXiv:2305.08768)

added reference

]]>added pointer to today’s

- Stéphane Peigné
*Introduction to color in QCD: Initiation to the birdtrack pictorial technique*[arXiv:2302.07574]

minor addition to “variants” section

]]>added this pointer:

- Jeffrey Ellis Mandula,
*Diagrammatic techniques in group theory*, Southampton Univ. Phys. Dept. (1981) (cds:129911, pdf)

Added to the Examples-section a pointer to *quantum circuit diagram*.

Finally, I took the liberty of reverting the renaming of the section title “Variants” (which John had changed to “Variants and Examples”): There is a section “Examples” right below, and there is a good point not to mix up variants of the general theory with examples.

So, instead, I now moved the example that John had silently added, namely “spin networks” to a new subsection “Examples – In representation theory” (here)

]]>I ended up editing the Idea section and re-instantiating pointer to Penrose notation right there at the beginning. I think this is what many readers who don’t already know about categories, let alone monoidal categories, will need to hear first to get, as it were, the idea of the subject. Also, this is the honest attribution of the idea (it’s easy to take any grand idea and generalize its context a tad more, and it’s close to trivial if the grand idea was all about abstracting away from its context in the first place!).

Now the idea-section starts out as follows, which should hopefully be uncontroversial:

String diagramsconstitute a graphical calculus for expressing operations in monoidal categories. In the archetypical cases of the Cartesian monoidal category of finite sets this is Hotz’s notation (Hotz 65) for automata, while for finite-dimensional vector spaces with their usual tensor product this is Penrose’s notation (Penrose 71a, Penrose-Rindler 84) for tensor networks; but the same idea immediately applies more generally to any other monoidal category and yet more generally to bicategories, etc.

Also, I added captures of three figures from three original articles (Hotz, Penrose, Penrose-Rindler) flowing alongside the text. (All in the Idea-section here)

]]>Then let’s at least move it up to the top of the list of examples, certainly before mentioning of bicategories et al. I have moved the paragraph to here and adjusted a little.

]]>Clarified that tensor networks are a special case of string diagrams.

]]>Clarified that tensor networks are a special case of string diagrams.

]]>Added Jamie et al.’s paper as well as corrected some error involving on proof nets

Cole

]]>fix reference to CDH paper (thanks for adding it!)

Antonin Delpeuch

]]>Added the reference,

- Cole Comfort, Antonin Delpeuch, Jules Hedges,
*Sheet diagrams for bimonoidal categories*, (arXiv:2010.13361)

Added

- George Kaye,
*The Graphical Language of Symmetric Traced Monoidal Categories*, (arXiv:2010.06319)

Broken link fixed.

Matteo Durante

]]>added to the list of examples (here) a pointer to *’t Hooft double line notation*

added pointer to

- Predrag Cvitanović,
*Group Theory: Birdtracks, Lie’s, and Exceptional Groups*, Princeton University Press July 2008 (PUP, birdtracks.eu, pdf)

added these pointers:

Jacob Biamonte, Ville Bergholm,

*Tensor Networks in a Nutshell*, Contemporary Physics (arxiv:1708.00006)Jacob Biamonte,

*Lectures on Quantum Tensor Networks*(arXiv:1912.10049)

started an Examples-section (here)

For the moment it contains nothing but pointers to entries on Lie theory that show some string diagrammatics.

But if any entry deserves a good supply of graphical examples, it is this one here, and so maybe a stub entry named “Examples” reminds/motivates someone to add such.

]]>added publication data for this reference:

- Peter Selinger,
*A survey of graphical languages for monoidal categories*, in: Bob Coecke (ed.)*New Structures for Physics*, Lecture Notes in Physics, vol 813. Springer, Berlin, Heidelberg (2010) (arXiv:0908.334, doi:10.1007/978-3-642-12821-9_4)

Okay, I found those birdtracks:

one needs to

1) go to birdtracks.eu

2) then choose “webbook” from the menu on the left,

3) then click on the words “hyperlinked pdf” (which is not self-evident, as it’s not underlined)

4) then (one does not get a pdf but) one has to wait for the web display to load…

5) then finally scroll forward to page 8.

There is an “Example” which is actually where the “birdtracks” seem to be defined, and, at least on this and the following pages, they are just the standard Penrose/string diagram notation for tensor calculus in $(FinVect, \otimes)$.

This should be added to the entry on string diagrams. But I won’t do it.

]]>added publication data and links for this one:

- Ross Street,
*Categorical structures*, in: M. Hazewinkel (ed.),*Handbook of algebra – Volume 1*, Elsevier 1996 (pdf, 978-0-444-82212-3)