Goodwillie calculus and I

We study the implications of using the indexing category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. By careful analysis of the cross-effects of a reduced endofunctor of based spaces, this point of view leads to a monoidal model for the derivatives. Such structure induces operad and module structures for derivatives of monads and their modules, leading to a chain rule for higher derivatives. We also define a category through which n-excisive finitary functors to spectra factor, up to homotopy, and give a classification of such functors as modules over a certain spectral monoid.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Yeakel, Sarah A

Contributors dc:contributor

• McCarthy, Randy
• Ando, Matt
• Rezk, Charles
• Malkiewich, Cary

• Goodwillie calculus
• homotopy theory
• excisive functors

Statement dc:rights

• Copyright 2016 Sarah Yeakel

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/90811

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/90811