{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/130097"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/130097","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A categorical approach to interactions between mod 2 power operations","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","abstract_has_math":false,"creators":["Zhu, Heyi"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rezk, Charles W.","Heller, Jeremiah Ben","Stojanoska, Vesna","Berwick-Evans, Daniel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-16","date_published":"2025-07-16","updated_at":"2026-07-22T22:25:06Z","subjects":["Algebraic Topology","Primary Cohomology Operations In Algebraic Topology","Dyer-lashof Operations"],"languages":["en","eng"],"rights":["© 2025 Heyi Zhu All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/130097","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rezk, Charles W.","Heller, Jeremiah Ben","Stojanoska, Vesna","Berwick-Evans, Daniel"]},{"key":"dc:creator","label":"Author","values":["Zhu, Heyi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-16","2025-08"]},{"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 Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic Topology","Primary Cohomology Operations In Algebraic Topology","Dyer-lashof Operations"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["© 2025 Heyi Zhu All rights reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/130097"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","The student, Heyi Zhu, accepted the attached license on 2025-07-14 at 13:50.","The student, Heyi Zhu, submitted this Dissertation for approval on 2025-07-14 at 14:08.","This Dissertation was approved for publication on 2025-07-16 at 15:04.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22552 on 2025-10-25 at 15:30:59","We generalize the numerical formula due to Nishida which computes the effect of interchanging dual Steenrod operations and Dyer-Lashof operations acting on the homology of a space to a categorical relation between their A-based analogues over any given multiplicative cohomology theory A. Our approach interprets these two power operations as arising from comonadic and monadic structures on the homotopy category of A-modules. This perspective has the advantage of clearly identifying the computational input required to understand the interactions between these operations in concrete terms, given the choice of A—a feature not made explicit in previous work."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A categorical approach to interactions between mod 2 power operations"]}]}],"canonical_facts":{"dc:contributor":["Rezk, Charles W.","Heller, Jeremiah Ben","Stojanoska, Vesna","Berwick-Evans, Daniel"],"dc:creator":["Zhu, Heyi"],"dc:date":["2025-07-16","2025-08"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01","The student, Heyi Zhu, accepted the attached license on 2025-07-14 at 13:50.","The student, Heyi Zhu, submitted this Dissertation for approval on 2025-07-14 at 14:08.","This Dissertation was approved for publication on 2025-07-16 at 15:04.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22552 on 2025-10-25 at 15:30:59","We generalize the numerical formula due to Nishida which computes the effect of interchanging dual Steenrod operations and Dyer-Lashof operations acting on the homology of a space to a categorical relation between their A-based analogues over any given multiplicative cohomology theory A. Our approach interprets these two power operations as arising from comonadic and monadic structures on the homotopy category of A-modules. This perspective has the advantage of clearly identifying the computational input required to understand the interactions between these operations in concrete terms, given the choice of A—a feature not made explicit in previous work."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/130097"],"dc:language":["en","eng"],"dc:rights":["© 2025 Heyi Zhu All rights reserved."],"dc:subject":["Algebraic Topology","Primary Cohomology Operations In Algebraic Topology","Dyer-lashof Operations"],"dc:title":["A categorical approach to interactions between mod 2 power operations"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}