{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/98290"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/98290","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stabilizing spectral functors of exact categories","abstract":"This Dissertation was approved for publication on 2017-07-13 at 15:08.","abstract_html":"This Dissertation was approved for publication on 2017-07-13 at 15:08.","abstract_has_math":false,"creators":["Villeta-Garcia, Juan S"],"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, Matthew","Rezk, Charles","Malkiewich, Cary"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-09-29T17:52:21Z","date_published":"2017-09-29T17:52:21Z","updated_at":"2026-07-22T22:24:35Z","subjects":["Algebraic K-theory","Goodwillie calculus","Homotopy theory","Algebraic topology"],"languages":["en"],"rights":["Copyright 2017 Juan Villeta-Garcia"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/98290","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McCarthy, Randy","Ando, Matthew","Rezk, Charles","Malkiewich, Cary"]},{"key":"dc:creator","label":"Author","values":["Villeta-Garcia, Juan S"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-09-29T17:52:21Z","2019-09-30T09:15:23Z","2017-07-13","2017-08"]},{"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":["Algebraic K-theory","Goodwillie calculus","Homotopy theory","Algebraic topology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Juan Villeta-Garcia"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/98290"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This Dissertation was approved for publication on 2017-07-13 at 15:08.","We define and study the $K$-theory of exact categories with coefficients in endofunctors of spectra in analogy with Mitchell's homology of categories. Generalizing computations of McCarthy, we determine, for a discrete ring $R$, the $K$-theory of the exact category of finitely-generated projective $R$-modules with coefficients in the $n$-fold smash product functor. This computation allows us to analyze the effects of applying this functorial construction to the Goodwillie Taylor tower of a homotopy endofunctor of spectra. In the case of $\\Sigma^\\infty\\Omega^\\infty$, the associated tower recovers the Taylor tower of relative $K$-theory as computed by Lindenstrauss and McCarthy.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01","The student, Juan Villeta-Garcia, accepted the attached license on 2017-07-13 at 00:31.","The student, Juan Villeta-Garcia, submitted this Dissertation for approval on 2017-07-13 at 00:39.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11445 on 2017-09-29 at 11:19:20","Made available in DSpace on 2017-09-29T17:52:21Z (GMT). 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Generalizing computations of McCarthy, we determine, for a discrete ring $R$, the $K$-theory of the exact category of finitely-generated projective $R$-modules with coefficients in the $n$-fold smash product functor. This computation allows us to analyze the effects of applying this functorial construction to the Goodwillie Taylor tower of a homotopy endofunctor of spectra. In the case of $\\Sigma^\\infty\\Omega^\\infty$, the associated tower recovers the Taylor tower of relative $K$-theory as computed by Lindenstrauss and McCarthy.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01","The student, Juan Villeta-Garcia, accepted the attached license on 2017-07-13 at 00:31.","The student, Juan Villeta-Garcia, submitted this Dissertation for approval on 2017-07-13 at 00:39.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11445 on 2017-09-29 at 11:19:20","Made available in DSpace on 2017-09-29T17:52:21Z (GMT). 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