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Goodwillie Calculus

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If you have a question about this talk, please contact Nathanael Arkor.

Goodwillie Calculus is a categorification of differential calculus in which infinity categories are the analogue of smooth manifolds, with functors between them the analogue of continuous/differentiable functions. Goodwillie’s main contribution is a tower of successive “n-polynomial” functor approximations, whose colimit converges to the original functor under the right circumstances. The analogy, which goes deep, gives insights into a topos-theoretic treatment of stable homotopy theory that is amenable to HoTT. In this approach, stabilizing a category is the analogue of linearizing it. We will give an exposition of Goodwillie calculus, covering polynomial approximations and stabilization.

This talk is part of the Logic & Semantics for Dummies series.

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