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Because applied category theory stops at translating everything into boxes and arrows. There's no "applied Yoneda lemma."
by whatshisface 4y ago
Because applied category theory stops at translating everything into boxes and arrows. There's no "applied Yoneda lemma."
- lgdw 4y agoIt's the actual process of translating everything into boxes and arrows that's the core of ACT.
- larve 4y agoI'm not sure that's true. This is a surface / introductory article, but if you go deeper into say, categorical databases, modeling of attacks (https://arxiv.org/pdf/2103.00044.pdf https://arxiv.org/pdf/2103.00044.pdf), there sure is some wilder CT at work. I'm leaving out programming as applied category theory because there is no shortage of refined concepts there (type theory, all the haskell libraries, many things I don't even comprehend). But to me, the value in ACT is actually learning how "simple" some of the other fields could be, because it allows me to communicate with non-software engineers, and actually have them contribute to software. I did a lot of work with state machines as composable abstractions for concurrency and flow control, and mechanical engineers were able to find some really subtle say, race conditions, just by pointing out "hey, isn't there an arrow from this to this, if the limit switch catches early?"
- vladf 4y agolol, you picked the one thing category theory actually has examples of not being abstract nonsense for https://mathoverflow.net/questions/12511/what-is-yonedas-lemma-a-generalization-of https://mathoverflow.net/questions/12511/what-is-yonedas-lem...
- hackandthink 4y agoIn computing you can apply Yoneda for optimizations. "Each of the steps is fairly compelling, except perhaps the second one, which rests on the Yoneda Lemma" see "Kan Extensions for Program Optimisation" https://www.cs.ox.ac.uk/ralf.hinze/Kan.pdf https://www.cs.ox.ac.uk/ralf.hinze/Kan.pdf