Goodwillie calculus and I

Goodwillie calculus;homotopy theory;excisive functors

Yeakel, Sarah A

关键词: Goodwillie calculus;    homotopy theory;    excisive functors;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/90811/YEAKEL-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.