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Of course, the chain rule explained via differential topology is simply functoriality! IME, category theory was much more valuable in differential topology in
by siraben 5y ago
Of course, the chain rule explained via differential topology is simply functoriality!
IME, category theory was much more valuable in differential topology in helping solidify why the structures and their compositional properties make sense. You get to work with several, honest-to-god categories and functors between them, especially when tangent bundles come into the mix.
Now go to programming, there's really only one category at play, and I'm not sure how worthwhile it is to apply a (more contrived) version of CT that only has endofunctors and being cartesian closed.
- chobytes 5y agoHaha, I feel like thats how I started to get CT concepts too. Topology and geometry really feel like the "natural" context for those ideas. For programming... I feel like they're basically trying to do logic in a roundabout way. I suspect that (finite) model theory might be more useful for such applications if they really want theory.