Connor Malin: Koszul duality methods in functor calculus

Abstract:

Functor calculus is a technique to study functors by decomposing them into canonical towers of approximations. We reproduce some of Arone-Ching's results in two new settings: Goodwillie calculus of algebra categories and orthogonal calculus. In these settings, we construct the fake Taylor tower whose layers receive the norm map from the Goodwillie tower. We discuss applications to the Koszul duality of algebras and Poincaré/Koszul duality of \(E_n\) algebras.