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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
Degree Granting Institution:University of Illinois at Urbana-Champaign
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
Rights Information:Copyright 2016 Sarah Yeakel
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05

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