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McCarthy, Randy Ando, Matt Rezk, Charles Malkiewich, Cary Yeakel, Sarah A 2016-07-07T20:27:54Z 2016-07-07T20:27:54Z 2018-07-08T09:15:20Z 2016-04-21 2016-05 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. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01 The student, Sarah Yeakel, accepted the attached license on 2016-04-20 at 21:20. The student, Sarah Yeakel, submitted this Dissertation for approval on 2016-04-20 at 21:25. This Dissertation was approved for publication on 2016-04-21 at 10:09. DSpace SAF Submission Ingestion Package generated from Vireo submission #9390 on 2016-07-07 at 13:50:31 Made available in DSpace on 2016-07-07T20:27:54Z (GMT). No. of bitstreams: 3 YEAKEL-DISSERTATION-2016.pdf: 549530 bytes, checksum: d6f0e2b0bc7d8a7e91b6012914ffdfe0 (MD5) LICENSE.txt: 4209 bytes, checksum: 88bf07fb1003e46aeae48c601b9997cc (MD5) PROQUEST_LICENSE.txt: 4555 bytes, checksum: 403b62c60dc8ff63817eb467312d2f2f (MD5) Previous issue date: 2016-04-21 Embargo set by: Seth Robbins for item 93163 Lift date: 2018-07-07T20:28:14Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 93163 Lift date: 2018-07-07T20:35:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 93163 on 2018-07-08T09:15:20Z. application/pdf http://hdl.handle.net/2142/90811 en Copyright 2016 Sarah Yeakel Goodwillie calculus homotopy theory excisive functors Goodwillie calculus and I text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.