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A few years ago, I wrote a runtime typing library for javascript using concepts from category theory. Objects are contracts, functions that either are the identity or throw an exception. Morphisms are guarded functions, functions that run a contract over the input and output. If the input contract fails, it's the caller's fault; if the output contract fails, it's the function's fault.
There's a blog and a series of YouTube videos. I covered only the most introductory concepts. I might do some more videos if there's enough interest.
I've come across your series before. It's really interesting.