Resources on String Diagrams, and Adjunctions, and Kan Extensions

I’ve been trying to figure out Kan Extensions

Ralf Hinze on Kan Extensions


But while doing that I went down a rabbit hole on String Diagrams

This post is the first one on String Diagrams that made sense to me.

I had seen this stuff before, but I hadn’t appreciated it until I saw what Haskell expressions it showed equivalence between. They are not obvious equivalences

This seems like a very useful video on this topic.

In Summary, it is an excellent notation for talking about transformations of a long sequence of composed Functors¬† F G H … into some other long sequence of Functors. The conversion of functors runs from up to down. The composition of functors procedes left to right.¬† F eta is the fmap of eta, and eta F is eta with the forall’ed type unified to be of the form F a.

Adjunctions L -| R are asymmetric between cups and caps. L is on the left in cups and on the right in caps. That’s what makes squiggles pull straightable

I think I have an interesting idea for a linear algebra library based on this stuff


John Baez and Mike Stay’s Rosetta Stone (A touch stone I keep returning to)

Dan Piponi gave a talk which is another touch stone of mine that I come back to again and again. There is a set of corresponding blog posts.

Other resources:

NCatLab article

John Baez hosted seminars



Dan Marsden’s Article

Marsden and Hinze have been collaborating

Stephen Diehl on Adjunctions


A Section From an old Oregon Programming Language Summer School (a rich set of resources)


Marsden and Hinze have been collaborating


Mike Stay doing a very interesting series of Category Theory in Javascript. He uses contracts in place of types. Defeats one of the big points of types (static analysis), but still pretty cool



I think that about covers everything I know about.

Oh yeah, there is the whole Coecke and Abramsky categorical quantum mechanics stuff too.

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