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the functorivative is the universal cone of the Goodwillie calculus/divided power structures? But what about subtraction -- in the definition of the numerical derivative? No problem: https://arxiv.org/abs/1808.06006 An Einfty Eckmann-Hilton argument.
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The functorivative gets imaged in algorithms, we automatically differentiate the algorithm https://en.m.wikipedia.org/wiki/Automatic_differentiation … then we lift back into the appropriate categories so that all the types are correct.
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