[–] marxshrugged 11y ago ↗ I am still trying to wrap my head around this, but the parallels with functional programming are striking. [–] Garlef 11y ago ↗ String diagrams are a way to describe morphisms (think functions) in monoidal categories.A construction using monoidal categories (or a slight generalisation) can be used to give a categorical model for arrows.http://bentnib.org/arrows.pdfThis gives rise to these diagrams:https://www.haskell.org/arrows/
[–] Garlef 11y ago ↗ String diagrams are a way to describe morphisms (think functions) in monoidal categories.A construction using monoidal categories (or a slight generalisation) can be used to give a categorical model for arrows.http://bentnib.org/arrows.pdfThis gives rise to these diagrams:https://www.haskell.org/arrows/
[–] kzrdude 11y ago ↗ This reminds me of something I never understood fully: Penrose's tensor notation.
[–] mrcactu5 11y ago ↗ I am guessing these diagrams are taken from Electrical Engineering and not Quantum Physics.The blog looks like an expansion of their paper http://arxiv.org/abs/1403.7048v3Yes! That's where I have seen these diagrams before. They are Hopf algebras, which appear both in Electrical Engineering and Theoretical Physics. [–] JadeNB 11y ago ↗ Baez discussed the paper on the n-Category Café, and it may be easier for the inexperienced (like me!) to get started there: https://golem.ph.utexas.edu/category/2015/05/props_for_linea... .
[–] JadeNB 11y ago ↗ Baez discussed the paper on the n-Category Café, and it may be easier for the inexperienced (like me!) to get started there: https://golem.ph.utexas.edu/category/2015/05/props_for_linea... .
[–] lisper 11y ago ↗ Best to start at the beginning and read through:http://graphicallinearalgebra.net
[–] Garlef 11y ago ↗ Very impressive if the author developed this by himself. But this is a well known idea from category theory:http://en.wikipedia.org/wiki/String_diagram
7 comments
[ 381 ms ] story [ 185 ms ] threadA construction using monoidal categories (or a slight generalisation) can be used to give a categorical model for arrows.
http://bentnib.org/arrows.pdf
This gives rise to these diagrams:
https://www.haskell.org/arrows/
The blog looks like an expansion of their paper http://arxiv.org/abs/1403.7048v3
Yes! That's where I have seen these diagrams before. They are Hopf algebras, which appear both in Electrical Engineering and Theoretical Physics.
http://graphicallinearalgebra.net
http://en.wikipedia.org/wiki/String_diagram