{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/90811"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/90811","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Goodwillie calculus and I","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Yeakel, Sarah A"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["McCarthy, Randy","Ando, Matt","Rezk, Charles","Malkiewich, Cary"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T20:27:54Z","date_published":"2016-07-07T20:27:54Z","updated_at":"2026-07-22T22:26:34Z","subjects":["Goodwillie calculus","homotopy theory","excisive functors"],"languages":["en"],"rights":["Copyright 2016 Sarah Yeakel"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/90811","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McCarthy, Randy","Ando, Matt","Rezk, Charles","Malkiewich, Cary"]},{"key":"dc:creator","label":"Author","values":["Yeakel, Sarah A"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-07-07T20:27:54Z","2018-07-08T09:15:20Z","2016-04-21","2016-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Goodwillie calculus","homotopy theory","excisive functors"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Sarah Yeakel"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/90811"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We study the implications of using the indexing category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. 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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). 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