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Most of my exposure to using categorical results to design algorithms, is through modularity in functional programming. I am wondering whether there are examples where the proof of existence of polynomial-time algorithms went through category theory, where the algorithmic question isn't some form of thinly veiled canonicity/normalization statement. Is there an algorithm where the correctness of the algorithm relies on categorical constructions, the algorithm itself is practical to execute and the problem statement isn't categorical in nature?

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