|Location:||MSRI: Simons Auditorium|
I will describe a variety of models for the Goodwillie derivatives that have additional structure, principally as some kind of module over an operad. These module structures can be used to describe a chain rule for Goodwillie calculus. I will also try to explain how these constructions can be used to classify functors (up to Taylor tower equivalence) in terms of their derivatives. Our models are built from various natural transformation objects in the underlying category of functors, and the main theme for the talk will be on techniques for calculating such objects.