Topology and Geometric Group Theory Seminar
Many objects of interest in algebraic topology may be viewed as functors, which often makes them difficult to analyse directly. Functor calculus provides a means by which to approximate a certain type of functor F with a tower of `degree n' functors under F that is analogous to the Taylor series of a function. However, each type of functor calculus differs in its notion of what it means for a functor to be degree n, and in the type of functor to which it applies.
I will present results necessary for developing a more universal framework for functor calculus. As a first example we show how the discrete functor calculus of Bauer, Johnson and McCarthy may be placed into the context of simplicial model categories, allowing for a direct comparison to Goodwillie's original functor calculus.
This is joint work with Julia Bergner, Lauren Bandklayder, Brenda Johnson and Rekka Santhanam.
There will be a pretalk by J.D. Quigley at 12:15.