Files in this item

FilesDescriptionFormat

application/pdf

application/pdfYEAKEL-DISSERTATION-2016.pdf (550kB)Restricted to U of Illinois
(no description provided)PDF

Description

Title:Goodwillie calculus and I
Author(s):Yeakel, Sarah A
Director of Research:McCarthy, Randy
Doctoral Committee Chair(s):Ando, Matt
Doctoral Committee Member(s):Rezk, Charles; Malkiewich, Cary
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2016-04-21
Type:Thesis
URI:http://hdl.handle.net/2142/90811
Rights Information:Copyright 2016 Sarah Yeakel
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05


This item appears in the following Collection(s)

Item Statistics