# Goodwillie approximations to higher categories

Goodwillie approximations to higher categories

Speaker: Gijsbert Heuts, Harvard University

Abstract:
We show how to extend the machinery of Goodwillie calculus to build polynomial approximations to a certain class of higher categories, rather than to functors. These approximations enjoy universal properties with respect to polynomial functors. We provide a classification of Goodwillie towers of higher categories in terms of the derivatives of the identity functor. This classification can be used to study various localizations of unstable homotopy theory, e.g. rational homotopy theory, but also "periodic" localizations.