{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/116237"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/116237","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Quasicategorical Galois theories","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","abstract_has_math":false,"creators":["Rennie, Robert Joseph"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rezk, Charles","Stojanoska, Vesna","Ando, Matthew","Heller, Jeremiah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-08","date_published":"2022-08","updated_at":"2026-07-22T22:24:55Z","subjects":["quasicategorical Galois theorem","higher category theory","Galois theory","duality","quasicategory","enhanced mapping space","Segal groupoid","Segal groupoid object","internal presheaves","splitting object","splitting algebra"],"languages":["en","eng"],"rights":["Copyright 2022 Robert Rennie"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/116237","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rezk, Charles","Stojanoska, Vesna","Ando, Matthew","Heller, Jeremiah"]},{"key":"dc:creator","label":"Author","values":["Rennie, Robert Joseph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-08","2022-07-14"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"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":["quasicategorical Galois theorem","higher category theory","Galois theory","duality","quasicategory","enhanced mapping space","Segal groupoid","Segal groupoid object","internal presheaves","splitting object","splitting algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Robert Rennie"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/116237"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","The student, Robert Rennie, accepted the attached license on 2022-07-14 at 00:28.","The student, Robert Rennie, submitted this Dissertation for approval on 2022-07-14 at 01:01.","This Dissertation was approved for publication on 2022-07-14 at 15:09.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18296 on 2022-11-15 at 18:21:00","The classification of 1-toposes given by [Joyal-Tierney '84] admits a proof with a `categorical Galois theorem' playing a central role, as discussed in Galois Theories by Francis Borceux.. Our main result, Theorem 2.4.3, refines this result to a `quasicategorical Galois theorem.' Before we state and prove our main result, we expand upon the Mathematical content, and applicability, of the 1-categorical analogue. Specifically, we show how to begin with a duality result, and produce an application of the 1-categorical Galois theorem which mirrors the classical Galois theory of fields, rings, and covering spaces. We also offer a broadly accessible motivation for the 1-categorical Galois theorem, and hence for our quasicategorical Galois theorem. Finally, the proof of our main result is written as explicitly as possible toward the eventual goal of a model-independent generalization."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Quasicategorical Galois theories"]}]}],"canonical_facts":{"dc:contributor":["Rezk, Charles","Stojanoska, Vesna","Ando, Matthew","Heller, Jeremiah"],"dc:creator":["Rennie, Robert Joseph"],"dc:date":["2022-08","2022-07-14"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms","The student, Robert Rennie, accepted the attached license on 2022-07-14 at 00:28.","The student, Robert Rennie, submitted this Dissertation for approval on 2022-07-14 at 01:01.","This Dissertation was approved for publication on 2022-07-14 at 15:09.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18296 on 2022-11-15 at 18:21:00","The classification of 1-toposes given by [Joyal-Tierney '84] admits a proof with a `categorical Galois theorem' playing a central role, as discussed in Galois Theories by Francis Borceux.. Our main result, Theorem 2.4.3, refines this result to a `quasicategorical Galois theorem.' Before we state and prove our main result, we expand upon the Mathematical content, and applicability, of the 1-categorical analogue. Specifically, we show how to begin with a duality result, and produce an application of the 1-categorical Galois theorem which mirrors the classical Galois theory of fields, rings, and covering spaces. We also offer a broadly accessible motivation for the 1-categorical Galois theorem, and hence for our quasicategorical Galois theorem. Finally, the proof of our main result is written as explicitly as possible toward the eventual goal of a model-independent generalization."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/116237"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Robert Rennie"],"dc:subject":["quasicategorical Galois theorem","higher category theory","Galois theory","duality","quasicategory","enhanced mapping space","Segal groupoid","Segal groupoid object","internal presheaves","splitting object","splitting algebra"],"dc:title":["Quasicategorical Galois theories"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:55Z"}