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arXiv · 2104.12604

Goodwillie Calculus and Geometric Stacks

Renaud Gauthier
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Abstract

We show Goodwillie's calculus of functors and $n$-geometric $D^{-}$-stacks share similar features by starting to focus on the convergence of Taylor towers for homotopy functors and the fact that $\mathbb{R} F(A) \cong \text{holim} \mathbb{R} F(A_{\leq n})$ for geometric stacks, where $\{ A_{\leq n} \}$ provides a Postnikov tower of some given $A \in s \text{k-Alg}$. From there we show parallel results, such as similar homotopy fibers of connecting maps in towers, as well as polynomial approximations, pointwise approximations and reconstruction theorems for towers.

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Renaud Gauthier. 2021-04-26. Goodwillie Calculus and Geometric Stacks. https://arxiv.org/abs/2104.12604

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