Goodwillie Calculus and Geometric Stacks
Renaud Gauthier

TL;DR
This paper explores the parallels between Goodwillie calculus of functors and the theory of geometric stacks, focusing on convergence, tower approximations, and homotopy limits in a homotopical algebraic context.
Contribution
It establishes a conceptual link between Goodwillie calculus and geometric stacks, demonstrating similar properties and convergence behaviors in their respective tower constructions.
Findings
Homotopy limits of functors relate to Postnikov towers of stacks
Parallel structures in homotopy fibers of towers
Reconstruction theorems for polynomial approximations
Abstract
We show Goodwillie's calculus of functors and -geometric -stacks share similar features by starting to focus on the convergence of Taylor towers for homotopy functors and the fact that for geometric stacks, where provides a Postnikov tower of some given . 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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory
