Goodwillie calculus and I

Yeakel, Sarah A

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https://hdl.handle.net/2142/90811 Copy

Description

Title

Goodwillie calculus and I

Author(s)

Yeakel, Sarah A

Issue Date

2016-04-21

Director of Research (if dissertation) or Advisor (if thesis)

McCarthy, Randy

Doctoral Committee Chair(s)

Ando, Matt

Committee Member(s)

• Rezk, Charles
• Malkiewich, Cary

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Goodwillie calculus
• homotopy theory
• excisive functors

Abstract

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.

Graduation Semester

2016-05

Type of Resource

text

Permalink

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

Copyright and License Information

Copyright 2016 Sarah Yeakel

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